0 00:00:02,310 --> 00:00:06,420 Jorge Pullin: Okay, so let's begin today's been a different city who speak about Edge Mode mojo gravity. 1 00:00:07,379 --> 00:00:09,150 Daniele Pranzetti: Alright, so thank you very much for joining. 2 00:00:11,309 --> 00:00:12,420 Daniele Pranzetti: Today and learn present 3 00:00:13,620 --> 00:00:15,750 Daniele Pranzetti: Some new ideas about 4 00:00:17,970 --> 00:00:21,960 Daniele Pranzetti: Different way to think about Greg both of the classical and a quantum level. 5 00:00:23,220 --> 00:00:28,620 Daniele Pranzetti: This is work which has been done in collaboration with several authors this around and 6 00:00:29,850 --> 00:00:40,200 Daniele Pranzetti: Started with a paper with Andrew, which they are continuing with that data and, more recently, we started a series of papers with Mark and run 7 00:00:41,400 --> 00:00:50,790 Daniele Pranzetti: In title elements of gravity and unfortunately they managed to put the first two papers of the series online in time, but they should appear soon and 8 00:00:51,570 --> 00:01:05,490 Daniele Pranzetti: I think this is a place where we are. We have reached the clear, clear, is understanding how the new proposal that we were suggesting, but let me start with some perspective so 9 00:01:06,540 --> 00:01:14,160 Daniele Pranzetti: In our quest for quantum gravity and essential task is to reach a problem the standing of degrees of freedom and the seamlessness of gravity associated with 10 00:01:15,030 --> 00:01:24,510 Daniele Pranzetti: Local sub regions. Now there are free interlaced insights around this. One of the questions which are quite important for the rest of the talk and 11 00:01:24,990 --> 00:01:35,340 Daniele Pranzetti: On one hand, we have the insight about the local graphic behavior of generativity and this stems from the idea that black course carry geometrical entropy proportion to the area. 12 00:01:36,840 --> 00:01:51,570 Daniele Pranzetti: On the other hand, there is a deep experience with doing canonical gravity that jar is a constraint system. Now, this means that the total energy associated to any specific region, for instance, for any arbitrary time flow is entering quarter in this boundary 13 00:01:53,550 --> 00:02:02,490 Daniele Pranzetti: And then there is a third ingredient which is more recent and it's the understanding that we can assign traditional edge modes. When the boundary surfacing space. 14 00:02:03,210 --> 00:02:11,790 Daniele Pranzetti: Of course, this requires identify your boundary symmetry algebra associated with any surface and understand and agree additional modes as its representation states. 15 00:02:12,810 --> 00:02:19,500 Daniele Pranzetti: So I'm going to be, of course, much more specific about what I mean this is just give you general framework so 16 00:02:20,760 --> 00:02:27,570 Daniele Pranzetti: They interesting these insights best leads naturally good picture that the relevant geometrical degrees of freedom leave on boundaries. 17 00:02:28,710 --> 00:02:39,660 Daniele Pranzetti: That the dynamics and the fabric of space itself is encoding to the entanglement and the central point is that disentangle is derived from the fusion properties of the traditional boundaries in yogic 18 00:02:40,650 --> 00:02:51,450 Daniele Pranzetti: So this is some of the new perspective that we're trying to propose and trying to develop through the talk. And I want to say that this renewed interest in understanding 19 00:02:52,890 --> 00:03:10,110 Daniele Pranzetti: The nature and the dynamics of degrees of freedom fighting boundaries as being very active recently in the world. Not so easy. In fact, it's been a few years already. And there are quite a few papers is just a sample of work and, in particular, there's a lot of TV along on the slide. 20 00:03:12,090 --> 00:03:16,050 Daniele Pranzetti: Okay, so it's good to slay on the free now let me 21 00:03:18,030 --> 00:03:25,950 Daniele Pranzetti: Make a point for regiment. First of all, with Eastern Edge mode. So you can see an animal inch waist. You can see an Edge mode as 22 00:03:29,610 --> 00:03:35,760 Daniele Pranzetti: So from my perspective. So yeah, you can see from him as a contact in momentum to a boundary church. 23 00:03:36,660 --> 00:03:44,730 Daniele Pranzetti: And at the same time as was mentioned for you can see a service official states of the boundaries in the algebra. Now these white is somehow 24 00:03:45,150 --> 00:03:55,680 Daniele Pranzetti: Can be understood as the usual burritos, the correspondents, I will again I will be more specific and clear understanding of this definition but 25 00:03:56,220 --> 00:04:06,330 Daniele Pranzetti: Not from the perspective of canonical framework Punjab, which, as well as the describe the propagation pollution time with the geometry Edge Mode leap on corners. 26 00:04:06,720 --> 00:04:18,330 Daniele Pranzetti: That is given to the boundary surfaces. Are we free region of space like upper surface and in the context of holography they are supposed to reflect and represent in degrees of freedom of the 3D geometry. 27 00:04:20,310 --> 00:04:20,790 Daniele Pranzetti: Now, 28 00:04:22,560 --> 00:04:37,470 Daniele Pranzetti: Since classical spacetime is fully as a manifold, which can be described as an atlas of charts or if you want physical damage as a Union have been estate space can also be model as the union of free new regions grew together for the interfaces. 29 00:04:38,160 --> 00:04:50,970 Daniele Pranzetti: Is somehow this this vision of winner of a quantum form. If you want and then one can emission gravity to be written best guess a theory of Edge Mode leaving on the boundary surfaces of these patches of pretty geometry. 30 00:04:52,170 --> 00:05:12,210 Daniele Pranzetti: And this is somehow similar philosophy towards the gap approach is based on and also just by looking at recently. And then this just lets best into picture or space as a network of bubbles, which should eventually need to quantum gravity is a dynamic whole network of quantum edge months. 31 00:05:13,710 --> 00:05:29,550 Daniele Pranzetti: Now this picture, picture is naturally compatible. We love holography and it's the same to offer. If you want a perfect segue into sorry corresponding of gravity, both of the classical the country levels. Now the main reason why I want to spec good course winning property is that 32 00:05:31,320 --> 00:05:36,690 Daniele Pranzetti: Because we propose to label the states by boundary symmetry charges. And then, of course, bringing all 33 00:05:37,620 --> 00:05:44,700 Daniele Pranzetti: Of these charges of symmetry is a more rigorous selection process, in a sense, because it can be implemented as a fusion of symmetry algebra. 34 00:05:45,360 --> 00:05:58,680 Daniele Pranzetti: And there is a lot of work in this direction for instant by Bianca and operators and what I'm going to present the rest is not a reformulation at the macro level of gravity along those terms. 35 00:06:01,500 --> 00:06:04,980 Daniele Pranzetti: So let me go to Slide number for now. 36 00:06:07,590 --> 00:06:17,010 Daniele Pranzetti: So why edge modes. Okay, let's look at more from your system. We know that in quantum field theory, we need to introduce a cut off. 37 00:06:17,520 --> 00:06:24,720 Daniele Pranzetti: Which means basically to democratize it and then we need to learn how to remove this cut off without breaking the cemeteries. 38 00:06:25,350 --> 00:06:33,810 Daniele Pranzetti: So one resolution is to put the system on the lattice. Now the lattice can be understood as the partition of space into sub regions, if you want. 39 00:06:34,770 --> 00:06:43,890 Daniele Pranzetti: And the boundaries of the Rockies corresponds basically to the building. So the bond is corresponds to the building block of the law is what charges can be defined and the gauge the meeting. 40 00:06:44,400 --> 00:06:51,090 Daniele Pranzetti: Gets the form the sense that it's replaced by a lot is version of the gauge cemetery, which is necessary to the presence of the cutoff. 41 00:06:51,840 --> 00:07:00,060 Daniele Pranzetti: Is this a clear example of this is in the meals, where the continuum, the electric field community itself and its continued momentum is a 42 00:07:00,450 --> 00:07:12,060 Daniele Pranzetti: Connection field. And then when you go to the descriptor case, the electric field gets me a lot edges of the lattice and becomes on community and the gauging valiant in the continuum then is replaced by largest portion 43 00:07:13,290 --> 00:07:17,070 Daniele Pranzetti: Where are the some of the, let me let me practice as to bash 44 00:07:18,120 --> 00:07:23,970 Daniele Pranzetti: So this is something separate from your picture and effect. Now go to Slide number five. 45 00:07:27,000 --> 00:07:27,810 Daniele Pranzetti: I could you sum up 46 00:07:27,840 --> 00:07:29,430 Abhay Ashtekar: He said, I asked you a question. 47 00:07:32,190 --> 00:07:35,580 Abhay Ashtekar: I'll just the general philosophy. I just want to make sure I don't miss something so 48 00:07:36,780 --> 00:07:45,960 Abhay Ashtekar: So this, this idea that you so nicely presented in the last few slides that you know that the edge morsel living on this kind of these two surfaces. Right. 49 00:07:46,770 --> 00:07:47,400 Daniele Pranzetti: Yes, yes. 50 00:07:47,910 --> 00:07:59,940 Abhay Ashtekar: But so what is different from what everybody has been has been doing right any fun just consider city district ization like for example, tetra hydro, we always said that the area leaves on this boundary and 51 00:08:03,030 --> 00:08:05,790 Abhay Ashtekar: So this is same, or is there some new new idea. 52 00:08:05,850 --> 00:08:07,470 Daniele Pranzetti: That no no no. It did. 53 00:08:08,670 --> 00:08:14,760 Daniele Pranzetti: In fact, I'm gonna, I want to take this idea very seriously and the different is that I'm going to, I want to 54 00:08:16,110 --> 00:08:22,230 Daniele Pranzetti: Develop this idea in the continuum picture not in the discrete setting, but it is along the same lines. Absolutely. 55 00:08:22,950 --> 00:08:23,580 Abhay Ashtekar: Okay, thank you. 56 00:08:25,770 --> 00:08:26,610 Daniele Pranzetti: So in fact, 57 00:08:28,500 --> 00:08:30,840 Daniele Pranzetti: A now. Okay. It's like number five. 58 00:08:33,600 --> 00:08:39,870 Daniele Pranzetti: So, energy is basic, basic set a formulation of gravity elegant meets now. 59 00:08:40,650 --> 00:08:49,230 Daniele Pranzetti: The key medical sector theory provides an elegant description can be geometry and where the dramatic operators admin spiritual states can be defined in terms of 60 00:08:49,890 --> 00:08:58,380 Daniele Pranzetti: A fundamental flexibility in these eventually leads to the speaking of the sweetness of the spectrum, which is one of the mirror sets of will continue it it's it's 61 00:08:59,130 --> 00:09:09,240 Daniele Pranzetti: Very exciting great result. And now I want to emphasize one thing that is that classically the knowledge of the flux in the buck. 62 00:09:09,990 --> 00:09:20,940 Daniele Pranzetti: Allows to reconstruct different field fully or however in the quantum theory, the flax becomes a smear great honor to the surface. 63 00:09:21,870 --> 00:09:35,160 Daniele Pranzetti: And so what it means is that we only have access to boundary flux, if you want. So, from this point of view, there is a suitable speed quantum numbers that we call those natural with includes information about abundant flux charge 64 00:09:36,870 --> 00:09:38,640 Daniele Pranzetti: So from this perspective, then 65 00:09:40,380 --> 00:09:42,660 Daniele Pranzetti: There is two questions, which 66 00:09:43,770 --> 00:09:55,440 Daniele Pranzetti: One can ask and one is can we understand the flux non committal activity in grabbing it from the continuum point of view, we know that there is a an understanding of this community from the discrete point of view. 67 00:09:56,130 --> 00:10:02,100 Daniele Pranzetti: And there are these paper or regionally by bike equations apart and then Morrison throat So Alejandro and 68 00:10:02,760 --> 00:10:10,590 Daniele Pranzetti: Pride new perspective on this problem, but we really would like to understand the design community from the continuum. And if you want to pull it 69 00:10:11,130 --> 00:10:25,140 Daniele Pranzetti: Has wrong with face it. We're not sort of quantum gravity without solving first $1 million problem, of course, in reference to the Millennium price question of the massive gap between your meals and their confinement, because we see that this I probably read the questions. In fact, 70 00:10:26,670 --> 00:10:42,180 Daniele Pranzetti: And. And then the second question is, so if the we only have access to the flux and demand theory, then is there to choose pin point number enough to reconstruct tangential frame field. This is a crucial question that we want to address. 71 00:10:43,470 --> 00:10:44,130 Daniele Pranzetti: In the continuum. 72 00:10:46,860 --> 00:10:48,810 Daniele Pranzetti: And so 73 00:10:52,410 --> 00:10:56,970 Daniele Pranzetti: Another motivation for business is the fact that we know it's been from approach. 74 00:10:58,980 --> 00:11:11,490 Daniele Pranzetti: was constructed to tackle the issue of or the nomics which we saw that it's a it is some ambiguity is in the sense of a there is a question of each covariance that 75 00:11:12,540 --> 00:11:25,980 Daniele Pranzetti: One is paint very well in the future. Could you and also definitional simple quantity using activity. So what at what speed from does is they provide a transition and Peter between boundary states where Lauren's empire is manifest in the park. 76 00:11:27,000 --> 00:11:37,530 Daniele Pranzetti: In the center is implemented from the get go the same time, we saw that the economic quantization program refugee provides basically the physical Kiera setting in which informs our summer to be interpreted 77 00:11:38,130 --> 00:11:47,250 Daniele Pranzetti: So recalling the canonical could use a space where a set to seize broken down to so true. When was the time engage as the boundary spaces infamous been 78 00:11:47,730 --> 00:11:53,850 Daniele Pranzetti: Of course a goal of crucial interest and there's been a lot of work along these lines, which eventually led to this not celebrated 79 00:11:54,300 --> 00:12:03,660 Daniele Pranzetti: In many map where covariance is recovered from embedding of a switcheroo into SF DC and. Now, one question though is, 80 00:12:04,410 --> 00:12:10,320 Daniele Pranzetti: That is still not clear some is the compatibility between the canonical me time constraint and this information. 81 00:12:11,310 --> 00:12:16,800 Daniele Pranzetti: In this sense, can we derive a spin for model from economic quantization. This is still an open question. If you want 82 00:12:17,430 --> 00:12:33,300 Daniele Pranzetti: And along those lines. Then from from an economic point of view, maybe what we really need is to construct the key management space where all the Lawrence generators can be represented as direct reports. So as answer the second question could 83 00:12:34,320 --> 00:12:36,630 Daniele Pranzetti: Probably important insights into the first issue. 84 00:12:39,870 --> 00:12:44,580 Daniele Pranzetti: So let me bring another piece of evidence which 85 00:12:46,470 --> 00:12:53,460 Daniele Pranzetti: Another if you want it is another feature of refugee which supports this holographic understanding of the flat charges. 86 00:12:54,150 --> 00:13:06,420 Daniele Pranzetti: And nearly. This is why did they actually got better connection arises from the introduction of a topological turn the action that does not change the classic official motion but eating uses economical transformation across space. 87 00:13:06,960 --> 00:13:13,080 Daniele Pranzetti: Now, the introduction of the connections are crucial ingredient to reveal the non legal representation of the charges. 88 00:13:14,100 --> 00:13:28,890 Daniele Pranzetti: And this would be clarified shortly. But I think it's most people are aware of this fact. Now what I want to point out here is the fact that the discussion on the transformation can be encoded in the appearance of a boundary free space there. 89 00:13:29,940 --> 00:13:39,090 Daniele Pranzetti: And these can be understood as an extension of the boundary space, which basically allows us to define boundary flat charges and to compute decimate the algebra. 90 00:13:40,440 --> 00:13:49,920 Daniele Pranzetti: In a very from the consumer point of view. And so what we witness is how the passage based interconnection formulation is intimately related 91 00:13:50,310 --> 00:14:04,500 Daniele Pranzetti: To the appearance of unknown vanishing turnover charges which is satisfying to me the algebra or reading the continuum theory and another aspect I want to point out, which might be a part of the obvious, but he can have important implication is that 92 00:14:05,820 --> 00:14:08,490 Daniele Pranzetti: The origin of the non competitive of the field. 93 00:14:10,290 --> 00:14:10,710 Daniele Pranzetti: Which 94 00:14:12,000 --> 00:14:20,340 Daniele Pranzetti: makes this interesting constraint on community is a direct consequence of the discrimination procedure that we use in a spin forms. 95 00:14:20,910 --> 00:14:31,200 Daniele Pranzetti: And it seemed to know community with the flag system canonical energy. So with what this suggested that it contained description of the flexes and community. 96 00:14:31,590 --> 00:14:45,930 Daniele Pranzetti: Will allow an understanding of human community structure of the same physical strength as well. From my point of view, the continuum theory and this can provide crucial insight to on how to reconcile the lorenzen environments with the presence of a fundamental left in theory. 97 00:14:47,370 --> 00:14:50,790 simone: Are you now doing these only in the time gauge or in an arbitrary 98 00:14:51,840 --> 00:14:57,930 Daniele Pranzetti: Yeah, so I'm gonna start reviewing the time gets case and then I will relax the time which 99 00:14:58,710 --> 00:15:00,210 simone: But the equation you wrote here. 100 00:15:00,510 --> 00:15:06,540 Daniele Pranzetti: This is why this is not enough time to engage this is true in a in general. 101 00:15:07,050 --> 00:15:07,890 simone: Right, okay. 102 00:15:09,720 --> 00:15:18,540 Daniele Pranzetti: Yeah, I'm going to review. First, the case on the language to see how this boundary charges appear and then I would go to the food court case. 103 00:15:19,350 --> 00:15:23,280 Laurent Freidel: Sorry, could you use your pointer to show which equation you talking about when you yeah 104 00:15:23,670 --> 00:15:24,930 Daniele Pranzetti: Yeah, yeah. Okay. 105 00:15:26,760 --> 00:15:27,420 Daniele Pranzetti: Right, so yeah. 106 00:15:30,420 --> 00:15:39,480 Daniele Pranzetti: Then Lend me an important thing in the rest for the for notation what by beta, what we mean is gamma minus one. So, I know it's a bit 107 00:15:41,070 --> 00:15:48,990 Daniele Pranzetti: Unusual convention. It's just 2% Muslim equations, be that will be upstairs to simplify that we we define it as the inverse of the meaty part 108 00:15:52,530 --> 00:15:54,630 Daniele Pranzetti: OK, so now 109 00:15:55,860 --> 00:16:09,360 Abhay Ashtekar: Just as a side to mark when you write lines open source over the reason why in many, many years did not use beta was because it was getting confused with the thermodynamics, right, the temperature and with the beta as it 110 00:16:09,570 --> 00:16:12,000 Abhay Ashtekar: Which copywriting hawking temperature and such and 111 00:16:12,000 --> 00:16:23,100 Abhay Ashtekar: Such and since this all the surfaces and horizons and such to relate to that temperature, you have to be really careful about the use of data. This is a very minus side point 112 00:16:23,520 --> 00:16:25,020 Daniele Pranzetti: Yeah, absolutely. Yeah. 113 00:16:26,940 --> 00:16:32,190 Daniele Pranzetti: Okay, so, um, so, from an organic perspective that we're proposing. 114 00:16:34,440 --> 00:16:45,690 Daniele Pranzetti: If the boundaries in theology is not big enough, then we cannot will account for all the degrees of freedom and we cannot hope for a buck reconstruction from the knowledge of the boundary charges so 115 00:16:46,410 --> 00:17:02,970 Daniele Pranzetti: It is clear, and once you look them up for a formulation that has the biggest one we seem to group. Now, the smallest and this extension corresponds basically to add the edge modes and it's encoded into the choice of the simplicity boundary potential. So the more extensive 116 00:17:04,170 --> 00:17:04,650 Daniele Pranzetti: Sorry. 117 00:17:05,760 --> 00:17:07,860 Daniele Pranzetti: Yes, the question yet highly 118 00:17:08,490 --> 00:17:22,740 lsmolin: High. So are you really claiming that for these situations with finite boundaries. He animals are enough to return to be given an equivalent formulation of dynamics to the boat and 119 00:17:23,460 --> 00:17:27,570 Daniele Pranzetti: That is the perspective, we're trying to propose, yes, making them with something 120 00:17:27,570 --> 00:17:36,960 lsmolin: Analogous to the strong around the same injection. That's about it is a fair amount entirely reasonable bite is a field on the edges on these finite 121 00:17:38,820 --> 00:17:39,540 Daniele Pranzetti: Yeah, I mean, 122 00:17:40,890 --> 00:17:50,130 Daniele Pranzetti: Philosophically is similar proposal, but yeah, we're not using specific boundary conditions and we're talking about local 123 00:17:51,750 --> 00:17:56,070 Daniele Pranzetti: sub regions not nothing topic. Yes. Okay. 124 00:17:56,400 --> 00:18:05,520 lsmolin: So you have a dynamics for these Edge mode which is equivalent to the dynamics in which your Gravity Forms for advocating and so forth. 125 00:18:06,420 --> 00:18:25,020 Daniele Pranzetti: That would mean i. So, in this token. Just going to present a documented medical case. And eventually, one would like to be able to recover or today dynamics of course strong from the buck from the boundary dynamics, but in in the rest of the book. And I'm going to focus mainly on them. 126 00:18:26,790 --> 00:18:32,460 Daniele Pranzetti: On the case with the yang mills in the dissertation to be more visible. 127 00:18:35,190 --> 00:18:35,580 Thank you. 128 00:18:37,260 --> 00:18:37,830 Daniele Pranzetti: So, 129 00:18:40,110 --> 00:18:48,930 Daniele Pranzetti: So best yet. So the more extended formulation. The bigger this the boundary algebra in the more we can reconstruct the bucket degrees of freedom. And then I'm extremely inspired 130 00:18:49,950 --> 00:18:55,770 Daniele Pranzetti: Now this bucket construction follows from the fact that the conservation of boundary charges. 131 00:18:57,540 --> 00:18:59,580 Daniele Pranzetti: Gives us an expression for tobacco strings. 132 00:19:00,720 --> 00:19:14,910 Daniele Pranzetti: In fact, I mean, this is going to be a one. One thing I'm gonna try to emphasize that we can understand that at least the canonical level constraint in the park as conservation low for boundary charges and so since 133 00:19:17,340 --> 00:19:29,160 Daniele Pranzetti: The dynamics of gratis more or less entire formulated in terms of constraints we need the maximum amount of material boundary seem interesting only to encapsulate of information about the economics. 134 00:19:29,790 --> 00:19:37,830 Daniele Pranzetti: And another reason why we should look for Maximus. Any theories forest from our experience with the composition of each theories, as was mentioned before. 135 00:19:38,130 --> 00:19:52,860 Daniele Pranzetti: That starts from the transition of bankruptcy or boats and the representations. So if you don't have a proper complete set of non tree or banners several then we don't really have a handle on on position and in this talk, we're going to see the benefits of this 136 00:19:53,940 --> 00:20:11,280 Daniele Pranzetti: Boundary for space extension by edge months in particular, what we're going to see is that the internal normal to a cushy surface becomes a dynamical Bible on the boundary free space, which can be understood as a for momentum of a new element upon carry algebra. 137 00:20:13,140 --> 00:20:19,710 Daniele Pranzetti: And the tangential metric becomes the canonical field which is necessary to reconstruct the tangential framer 138 00:20:21,270 --> 00:20:37,200 Daniele Pranzetti: Moreover, would see that the boundaries NPC constraint satisfy a second class algebra or reading the continuum and the correct position in terms of a first class piece and the one master constraint piece where it done is to break contrary Dr. Lawrence. 139 00:20:39,810 --> 00:20:57,390 Daniele Pranzetti: And then the the boundary area corresponds to the pond Craig's been cast me. So this means that its environment and the Lord and transformation and this reconciled is quickness of the spectrum, which is going to be derived from the content theory with the manifest Lawrence compare environments. 140 00:20:58,800 --> 00:21:09,870 Daniele Pranzetti: And finally, after position the constraints, the manifest space would be permit tries by a set of miracle server boats, which form, it's a module Pontic given by such Lucy. 141 00:21:10,740 --> 00:21:23,550 Daniele Pranzetti: Plus the search lot of the tangible metric, which basically means that we have two new quantum numbers on the boundary here space. So these are all the men restarted. I'm gonna industry in the rest of the book and you 142 00:21:23,790 --> 00:21:33,450 simone: Could you say a little bit more about the the first pointing the slide because like natively, one could think, think of the case of spatial infinity. 143 00:21:33,960 --> 00:21:49,860 simone: If one wants to have more than just the tempo encourage generators. One way would be to have stronger full of condition so that more charges are finite. But then this will lead to less solutions in the bank. 144 00:21:51,480 --> 00:21:53,010 simone: Can you say more on 145 00:21:53,580 --> 00:22:00,270 simone: So what we need to have more bulk dynamics from more from a larger boundary algebra. 146 00:22:02,310 --> 00:22:03,600 Daniele Pranzetti: So what I'm 147 00:22:05,160 --> 00:22:15,150 Daniele Pranzetti: Trying to say is that in order if you pre sense, look. Think of the switch recharges of quantum gravity, you should don't reveal those charges. 148 00:22:15,690 --> 00:22:33,390 Daniele Pranzetti: You will not be able to introduce an echo states right so that's what I'm trying to say that if you have a bigger boundary algebra, and then you're able to reveal more concrete numbers which can be used for the quantization of their to reconstruct the degrees of freedom. 149 00:22:35,160 --> 00:22:44,910 Daniele Pranzetti: Is that like gauging violence in the back, the Gauss law can be coded in the the some of the flags on the boundary to vanish and 150 00:22:44,970 --> 00:22:45,300 Laurent Freidel: And I 151 00:22:46,590 --> 00:23:00,960 Laurent Freidel: Yeah. Can I say something about that because we have a work without doing that shows that if you want or an extended the bigger Andrew brought infinity. In fact, that you don't need stronger boundary conditions you need weaker boundary conditions, but it's kind of where we can I 152 00:23:00,960 --> 00:23:01,260 Said, 153 00:23:02,640 --> 00:23:09,180 simone: I don't know what I meant to them, usually you would require stronger fall off. No. 154 00:23:09,180 --> 00:23:12,390 Laurent Freidel: No you you have to require less less full of condition. 155 00:23:12,450 --> 00:23:18,510 Abhay Ashtekar: Yeah, I think someone that is right. Right. Every week a boundary conditions gives you recharge. 156 00:23:20,190 --> 00:23:24,240 simone: You don't require the fields, go to zero faster in order to have more than just the 157 00:23:24,810 --> 00:23:28,080 Laurent Freidel: Not just, oh no, you require the exact opposite. But maybe that's 158 00:23:28,080 --> 00:23:29,910 Laurent Freidel: Another question we we cannot 159 00:23:31,020 --> 00:23:35,550 Abhay Ashtekar: Know i i agree with Laura completely. So maybe we can talk about this. The end. Yes. 160 00:23:35,670 --> 00:23:36,330 Laurent Freidel: Yeah, it's 161 00:23:37,590 --> 00:23:37,920 Daniele Pranzetti: Okay. 162 00:23:38,100 --> 00:23:48,690 lsmolin: Let me ask very nice question. So the claim. Now is that the boundary area corresponds to a chasm near the park array and therefore is boosting very 163 00:23:49,530 --> 00:24:02,460 lsmolin: So, so it doesn't correspond. I mean, I think in the older formulations, like the isolated rising picture was pretty clear that the boundary area we're accounting or spaceflight. 164 00:24:03,510 --> 00:24:12,180 lsmolin: And was not a Tasmania with that invariant, but the transform to somebody named Bruce pantry. So this is a different quality. 165 00:24:13,650 --> 00:24:14,730 Daniele Pranzetti: Not is there. 166 00:24:15,900 --> 00:24:18,720 Daniele Pranzetti: Is the same quantum is the same quantity. It's just that. 167 00:24:21,180 --> 00:24:23,070 Daniele Pranzetti: It's embedding a bigger 168 00:24:25,260 --> 00:24:26,370 Daniele Pranzetti: Symmetry. 169 00:24:27,360 --> 00:24:30,450 lsmolin: So here's my problem. If I have a city. 170 00:24:32,250 --> 00:24:44,460 Daniele Pranzetti: And it's it's normal to have vector. Can I make a difference transformation maker and spoon said that factor changes and therefore the to surface. 171 00:24:45,210 --> 00:25:03,120 Daniele Pranzetti: Area corresponds to changes. Yeah. You see the key point is that not the internal normal respect which you define that surface is dynamic. Also, it also gets altered rotated by the by the booster and that's why you restore its importance. 172 00:25:04,620 --> 00:25:10,500 Daniele Pranzetti: It's not they can what you're referring to is when a case in which the normal is a kinematics quantity that doesn't rotate 173 00:25:12,090 --> 00:25:12,360 Daniele Pranzetti: So, 174 00:25:12,870 --> 00:25:16,230 lsmolin: We're saying the opposite. But let's come back to this. 175 00:25:16,320 --> 00:25:16,740 Daniele Pranzetti: Yeah, I mean, 176 00:25:17,970 --> 00:25:20,100 Abhay Ashtekar: It's really one way to say this is that 177 00:25:21,000 --> 00:25:27,420 Abhay Ashtekar: What was done it, I sort of horizon etc etc is something that will happen in a fixed time gauge. Is that what you're saying. 178 00:25:28,140 --> 00:25:29,040 Daniele Pranzetti: Yeah, exactly. 179 00:25:29,190 --> 00:25:36,900 Daniele Pranzetti: Engaged yeah if you if you fix it engage. Then you recover the usual picturing which of course you don't have Lawrence him audience, right. 180 00:25:37,200 --> 00:25:47,850 Daniele Pranzetti: Okay, yeah, let's keep going. Yeah, this will, it will become. These are just the main reasons, man. It would be clear thinker, as we keep going. Yeah, so, um, 181 00:25:49,110 --> 00:26:00,180 Daniele Pranzetti: Now, let me first industry this pattern of teaching to breaking from the familiar case of data GST to flux. Now the main points that in the presence of the boundary, they may go slow is no longer 182 00:26:01,980 --> 00:26:16,860 Daniele Pranzetti: Differentiable and when you barely respect to the covering field. So in order to make a differential, you need to add the boundary there which defines the generator in this this expression here where sigma high is there, which are the two fields. 183 00:26:17,910 --> 00:26:24,870 Daniele Pranzetti: Now, if we impose a geographical zero then this is going to be true if alpha sigma 184 00:26:25,890 --> 00:26:35,790 Daniele Pranzetti: Vanish on the surface, which means basically that the gauging bias is broken in the presence of abundance. Now, there are several options to deal with this issue. 185 00:26:36,480 --> 00:26:45,450 Daniele Pranzetti: The first one is to simply which is someone most traditional one is to simply accept this fact and to promote the numbers, he charges to the status of a symmetry generators 186 00:26:46,830 --> 00:26:47,670 Daniele Pranzetti: Then there is the 187 00:26:49,380 --> 00:27:04,620 Daniele Pranzetti: Option, which basically one imposes that Jaffa vanishes only on a set of measured zero on the boundary which is represented by the punchers in this way, then the best tangential flux becomes 188 00:27:05,130 --> 00:27:13,260 Daniele Pranzetti: If you want senior in a sense that that the only charges left are the loop gallery flexes, which are associated with a with a puncher's 189 00:27:14,970 --> 00:27:20,550 Daniele Pranzetti: Now then, the third option that we want to follow is 190 00:27:21,630 --> 00:27:29,160 Daniele Pranzetti: Which leads to basically this loop run the picture we produce what a goal is to introduce Edge mode to restart the gauge symmetry. 191 00:27:30,120 --> 00:27:38,400 Daniele Pranzetti: And in this case, engage in violence is restore basically by extending the face face Emily by defining engagement stringent the data, which involves 192 00:27:38,820 --> 00:27:43,350 Daniele Pranzetti: The terms, depending on depart field that before the in black in this formula here. 193 00:27:44,250 --> 00:27:52,740 Daniele Pranzetti: But then it's also component, depending on the Edge nodes which I use it. I did not mean in a different font to make clear that these are 194 00:27:53,730 --> 00:27:57,750 Daniele Pranzetti: Boundary these features, edit, which are related. 195 00:27:58,230 --> 00:28:05,820 Daniele Pranzetti: To the boundary friendfield by the purity. These are independent fields that won't happen in order to restore gauging violence. In fact, then 196 00:28:06,090 --> 00:28:21,660 Daniele Pranzetti: One can see that the imposition of the this constraint to vanish imposes the gal from the bar class is increased equals three on the surface name is telling us that there's a continuity condition between the edge modes and the pullback of the offering field from the bug. 197 00:28:23,160 --> 00:28:27,900 Daniele Pranzetti: Which can be understood as a boundary simplicity constraint, if you want. So in this way, we can 198 00:28:29,940 --> 00:28:42,180 Daniele Pranzetti: We can define number two charges. So we're still getting violence. But the key point is that we can still define non vanishing sync recharges that act on the edge, what fields. 199 00:28:43,530 --> 00:28:49,740 Daniele Pranzetti: So these are the signatures and defining here and they basically 200 00:28:51,120 --> 00:29:02,820 Daniele Pranzetti: They in the coffin field is on the boundary remains dynamical and the letter G modes carry their own petty potential 201 00:29:03,750 --> 00:29:11,280 Daniele Pranzetti: In particular, they, they tried feel become some communities and we have the data non trivial representation of the boundary symmetry algebra. 202 00:29:11,940 --> 00:29:25,050 Daniele Pranzetti: So the key difference between this picture and some of the nice thing to bring teachers, they now become straightforward. Why does seem to charges the flexes become Norco community to satisfy the current algebra. 203 00:29:26,280 --> 00:29:29,220 Abhay Ashtekar: I'm confused about the notation here. So, yes. 204 00:29:29,310 --> 00:29:33,210 Abhay Ashtekar: Edge edge mortar. But the thing that they're tangential is that 205 00:29:33,900 --> 00:29:35,040 Daniele Pranzetti: Yes, yes. 206 00:29:35,070 --> 00:29:37,530 Abhay Ashtekar: Yes. So, therefore, that diet right no picture. 207 00:29:39,420 --> 00:29:40,230 Abhay Ashtekar: Died right 208 00:29:41,280 --> 00:29:42,990 Laurent Freidel: Well, yeah. 209 00:29:43,980 --> 00:29:45,270 lsmolin: tires on the to surface. 210 00:29:45,420 --> 00:29:50,760 Abhay Ashtekar: Yeah, he's a diet to surface. Yeah, so I'm confused about this index i 211 00:29:52,530 --> 00:29:58,410 Daniele Pranzetti: Not, I mean this space, the space time index is put back on the surface but internal index. 212 00:29:59,790 --> 00:30:02,580 Daniele Pranzetti: Is like the difficult for him field. 213 00:30:02,940 --> 00:30:04,350 Abhay Ashtekar: So it's not a diet. Okay. 214 00:30:04,410 --> 00:30:05,880 Daniele Pranzetti: No, no, no, no, it's 215 00:30:06,330 --> 00:30:11,130 Abhay Ashtekar: Not about it. Just a pullback in terms of the thing, but there are three into a good 216 00:30:11,220 --> 00:30:12,360 Daniele Pranzetti: Idea. Yeah. 217 00:30:12,690 --> 00:30:13,080 Sorry. 218 00:30:14,640 --> 00:30:21,780 lsmolin: It's not that the segment is that these I thought live on the on the boundary. And that's the point. Yeah. 219 00:30:22,380 --> 00:30:25,320 Daniele Pranzetti: Under but internal index is still expanding that 220 00:30:27,030 --> 00:30:28,170 lsmolin: Too. Yeah. 221 00:30:29,250 --> 00:30:31,710 Daniele Pranzetti: It is a one form on the boundary. Yes. 222 00:30:33,450 --> 00:30:48,120 Daniele Pranzetti: Yeah, yeah. Then they are so yeah well that means that they are related to the pool back of the tried on the market through the Gulf slow the biggest constraint, but they'd only live on the boundary. And that's why they 223 00:30:49,170 --> 00:30:57,450 Daniele Pranzetti: They only act on the they seem to charge a different here on the x on this element Bibles on the boundary 224 00:31:00,030 --> 00:31:00,780 Daniele Pranzetti: So, 225 00:31:03,450 --> 00:31:15,150 Daniele Pranzetti: Yes. And then I think that we can recover their non community. We have the flux algebra, but we're also going to see that this Edge Mode contains more information than just the flux that is one of the key point. 226 00:31:17,460 --> 00:31:17,880 Daniele Pranzetti: Now, 227 00:31:18,930 --> 00:31:31,830 Daniele Pranzetti: This idea of same logic of basic expressing kinematics constraint in the back so conservation looking also be extended to them to the momentum to the difficult string to defeat the difficult strength. 228 00:31:32,880 --> 00:31:42,480 Daniele Pranzetti: And but then we can see that in the present a boundary. We need to in order to have the day from a very simple straight to be differentiable, we need to include a boundary piece. 229 00:31:43,890 --> 00:31:59,820 Daniele Pranzetti: And and so what we can do is to replace the standard difficult thing with them momentum constraint which I wrote down here, which is equivalent to the imposition of the default constraint and 230 00:32:01,590 --> 00:32:17,010 Daniele Pranzetti: Then this constraint, then a contains a bad piece, this piece I G which are basically implements the different or constraint in the park and then there is a boundary piece, which again is, it's a symmetry. It's a charge they found the boundary 231 00:32:18,240 --> 00:32:28,110 Daniele Pranzetti: And this API is really defined here in the box is the best is the portion of the hashtag or a better connection. So this is the chart associated to three different phases. 232 00:32:28,920 --> 00:32:49,560 Daniele Pranzetti: And then we can see the different posts the bar component. This defines the the translation engagement stream which is equivalent to be from a physical by taking this say hi to be the construction of the vector of excite tangent to the surface with with their co free. Yeah. 233 00:32:50,580 --> 00:33:02,430 Daniele Pranzetti: And so in this way one can see that 50 different can be written as a conservation law for this church, which we call the sutra moment in charge, and they will be clear on the moment the physical meaning of this church. 234 00:33:03,990 --> 00:33:15,360 Daniele Pranzetti: Once a week, compared with the metric case. But this is just to say that this philosophy can be standing, not just to the gauge in the internet age minds, but also to feed the difficult strength. 235 00:33:16,560 --> 00:33:23,280 Abhay Ashtekar: But in this case is the philosophy or slightly different from the previous one. Because previously you added a new degree of freedom and the boundary 236 00:33:23,640 --> 00:33:31,890 Abhay Ashtekar: Yes. Your and then only kind of equations emotion told you that the new degree of freedom was related to the sigma by pullback right 237 00:33:32,340 --> 00:33:37,260 Abhay Ashtekar: Yes. Whereas, you're, you're not adding a new degree of freedom and you could add a new degree of freedom. 238 00:33:37,410 --> 00:33:43,710 Abhay Ashtekar: I could answer that the question emotion relate the new degree of freedom to be equal to what you call the I'm the 239 00:33:45,270 --> 00:33:48,450 Abhay Ashtekar: Equation below right but you're not doing that is there is 240 00:33:50,070 --> 00:33:51,330 Daniele Pranzetti: No, there is no 241 00:33:52,710 --> 00:33:57,690 Daniele Pranzetti: We haven't done that, in fact, and I was gonna say this in the next slide. 242 00:33:58,980 --> 00:34:02,730 Daniele Pranzetti: Yeah, it's fine. I mean, in fact, we can go to the next slide that maybe we can can so 243 00:34:03,750 --> 00:34:16,470 Daniele Pranzetti: We could have had those Edge mode for the momentum charges as well and they want, you could study how the imposition of the constraint leads to 244 00:34:17,070 --> 00:34:28,350 Daniele Pranzetti: Basically these identification lynch mobs with the bulk of the pushback from the market. The momentum, what we did instead was to follow or more energy approach for those charges, namely to introduce 245 00:34:29,970 --> 00:34:38,790 Daniele Pranzetti: Local sources of momentum and portion on the surface and then to quantifies the the the boundary 246 00:34:39,690 --> 00:34:50,730 Daniele Pranzetti: Degrees of freedom you using those boundary condition. So what we did so far is to treat it if you want curvature, especially curvature sources in as classical background structure. 247 00:34:51,180 --> 00:35:01,290 Daniele Pranzetti: And the momentum sources as a distribution or as you would do in quantum gravity for their for the flux. So, it was. It's an elaborate on decision that we need in order to 248 00:35:03,840 --> 00:35:06,120 Daniele Pranzetti: As the first step to the quantization of this boundary 249 00:35:07,170 --> 00:35:15,540 Daniele Pranzetti: Boundary face space, but the philosophy. Yes, will be the same that you keep adding Edge mode and then you can contest in from a content point of view. 250 00:35:16,950 --> 00:35:28,260 Daniele Pranzetti: The boundary degrees of freedom. But then, so the ideas and then will be the user with this Bible we bonded by surface which will be described the stream that can be understood. So 251 00:35:30,480 --> 00:35:40,500 Daniele Pranzetti: Some quantum jump to the log or subsystem and with this expectation of quantum space localized at the pictures were which includes some stranger charges. 252 00:35:41,220 --> 00:35:50,130 Daniele Pranzetti: And the states then associated with the region or representation states of the boundaries community group and each bubble of space is represented by adding the pointer. 253 00:35:51,150 --> 00:35:58,050 Daniele Pranzetti: Which represents the conservation law, the vertex of this boundary charges of course would get a generalized interpersonal justice between the webinar. 254 00:35:58,890 --> 00:36:05,130 Daniele Pranzetti: And then the this chunks of quantum space can be patched together by basically first flattening if you want this. 255 00:36:05,790 --> 00:36:17,280 Daniele Pranzetti: Ball to create the speed restructure you cylinders around the curvature defects which propriety propagate then by matching the quantum numbers of the punchers when this happens. 256 00:36:17,760 --> 00:36:28,770 Daniele Pranzetti: And then in a further step to achieving a more discreet picture is too coarse grain basically this algebra and free someone can choose to 257 00:36:30,060 --> 00:36:44,220 Daniele Pranzetti: Keep only the dual mode sector of this algebra, and we saw that if you do this, for instance, from this picture here, you end up with this point what we call our current networks which contain the control numbers bouncing additional momentum label associate exactly this. 258 00:36:45,780 --> 00:36:50,970 Daniele Pranzetti: Different more feasible or constraint charge. I was talking about before. So this is 259 00:36:52,230 --> 00:37:01,320 Daniele Pranzetti: This will be the philosophy of how to eventually glued together this local sub regions in order to a constructor state of quantum geometry for all the surface. 260 00:37:02,790 --> 00:37:13,710 Daniele Pranzetti: But so there were two key ingredients, as was noted already in this construction, which was the use of time gauge personal and the use of some discrete oneness in the center of this devotional 261 00:37:14,880 --> 00:37:17,070 Daniele Pranzetti: audition for the charges of momentum and 262 00:37:19,230 --> 00:37:24,660 Daniele Pranzetti: And from portion and the curvature. So what we want to do now is to somehow step back 263 00:37:25,860 --> 00:37:37,020 Daniele Pranzetti: And relax the assumption you can gauge where only the electric elements, corresponding to the rotation of part of the law or Lauren city were introduced and 264 00:37:39,300 --> 00:37:41,280 Daniele Pranzetti: We want to. Oh, like 265 00:37:42,870 --> 00:37:47,130 Daniele Pranzetti: Trying to unravel the Edge Mode structure of gravity from the continue on to you. 266 00:37:48,450 --> 00:37:57,660 Daniele Pranzetti: To have a clear understanding of what the food boundary simply algebra from the computer is and this eventually will allow us to derive all the physical direct server boats and 267 00:37:58,920 --> 00:38:07,410 Daniele Pranzetti: Eventually, to understand how the tangential frame can be reconstructed from this miracle server boards, both in the classical ending the quantum case. 268 00:38:08,670 --> 00:38:22,140 Daniele Pranzetti: And a first point that will show in a mom is that the different components of the symmetry group are revealed by different gravity formulations. But before getting there me just introduce a bit of meditation, so 269 00:38:23,940 --> 00:38:24,330 Daniele Pranzetti: Yeah. 270 00:38:24,600 --> 00:38:28,800 lsmolin: Just to clarify, because there are several things going on in the previous slide. 271 00:38:29,250 --> 00:38:29,760 Daniele Pranzetti: Yes. 272 00:38:29,790 --> 00:38:41,100 lsmolin: One of them is the choice to and I think this is a choice of boundary conditions to take the punctures two circles. 273 00:38:41,670 --> 00:39:06,240 lsmolin: And the edges two cylinders in a way that lets you introduce the category algebra or the, I guess the Lawrence plus Parker. A into which is what you mean by this little circle. So you go from one puncture where you represent some charge of the park or algebra to representing its 274 00:39:07,410 --> 00:39:13,470 Daniele Pranzetti: Current algebra, there were, there are now a circle and two degrees of freedom. Yeah. 275 00:39:14,100 --> 00:39:17,430 lsmolin: So I have a stage right what what what part of this movement. 276 00:39:18,270 --> 00:39:29,610 Daniele Pranzetti: Yeah, this is a, it's a binary condition. If you want is the distribution organization of curvature and ocean defects around punctures and then yet this regularization if you want of 277 00:39:31,350 --> 00:39:36,450 Daniele Pranzetti: These defects in terms of discs, which leads to this that's more the charges but 278 00:39:36,690 --> 00:39:39,420 Abhay Ashtekar: There is no sound. Can we can people hear 279 00:39:40,200 --> 00:39:42,120 Daniele Pranzetti: Can you, can you hear me or 280 00:39:43,620 --> 00:39:44,670 lsmolin: It was I hear me. 281 00:39:47,040 --> 00:39:49,350 Laurent Freidel: Yes, we can. I can hear. Okay. 282 00:39:49,530 --> 00:39:55,500 lsmolin: So my question is, why, why did you choose to do this. Is this a choice. 283 00:39:55,770 --> 00:40:05,430 lsmolin: Because we're the last find you take it away and you say, then truncate down to the final dimension algebra and I'm left wondering why is into that in the first place. 284 00:40:06,090 --> 00:40:17,610 Daniele Pranzetti: Or that it will recover. Like if you want to simplify things, and to do some cross training that show how the ecology limit can be recovered, but 285 00:40:18,810 --> 00:40:26,790 Daniele Pranzetti: To show that at the same time, if you do this truncation, you still end up with summit and one extra one to number which is this momentum charge 286 00:40:27,840 --> 00:40:34,350 lsmolin: Right, so I understand that. But when you resolve the singularity of the puncture is that 287 00:40:35,430 --> 00:40:40,260 lsmolin: That choice or is that somehow first time you buy some 288 00:40:41,010 --> 00:40:51,570 Daniele Pranzetti: Notes. If you want it. If you want to simplify your life and want to work just with the introduction of the algebra. That's how you can envision it but you don't have to course you can. 289 00:40:52,230 --> 00:40:54,540 lsmolin: simplify my life. I wouldn't be doing this but 290 00:40:54,960 --> 00:40:57,750 Daniele Pranzetti: Yeah, well, wait. 291 00:40:58,770 --> 00:41:00,210 Daniele Pranzetti: This is 292 00:41:00,510 --> 00:41:01,680 Laurent Freidel: Going to come. No, because 293 00:41:01,680 --> 00:41:01,920 Daniele Pranzetti: Yeah. 294 00:41:02,040 --> 00:41:07,350 Laurent Freidel: You know what you're going to do next is not doing any of these choices and redirecting to continue 295 00:41:07,860 --> 00:41:15,810 Laurent Freidel: You don't have to do these tours is, it's just these choices. The show how you go from do full continuum algebra to do energy 296 00:41:18,120 --> 00:41:18,420 Yeah. 297 00:41:20,040 --> 00:41:20,520 Okay. 298 00:41:22,140 --> 00:41:23,250 Daniele Pranzetti: Yeah, so 299 00:41:24,720 --> 00:41:27,930 Daniele Pranzetti: Meditation. So yes, we, we introduce 300 00:41:29,100 --> 00:41:39,600 Daniele Pranzetti: Space that man, which has a rental metric. And then we we do the free body composition with a dimension one slice sigma here. And then we have the 301 00:41:41,430 --> 00:41:49,020 Daniele Pranzetti: The normal one for n from which we can resolve the internal normal vector, and I would take. So this is a time like vector 302 00:41:49,860 --> 00:41:59,640 Daniele Pranzetti: And then they could do tangential co frame field can be a snotty with you still there. So all the qualities within the basically means a pullback on this slide, sigma 303 00:42:00,030 --> 00:42:08,430 Daniele Pranzetti: And so we have the news medical sigma with GTA. And then they induce metric on the boundary of sigma the corner would be denoted by a cute baby. 304 00:42:09,330 --> 00:42:22,890 Daniele Pranzetti: And the last bit of notation is this killed epsilon, which is basically used to define an inner product and internet space. So these are the quantities and I'm gonna use in the following 305 00:42:24,780 --> 00:42:28,320 Daniele Pranzetti: And OK, so now let's go to the next slide. 306 00:42:29,670 --> 00:42:39,720 Daniele Pranzetti: Now, so let's start with the metric formulation of gravity. And so the static points that the construction of the quality space feminism is this precipitous potential 307 00:42:41,850 --> 00:42:51,180 Daniele Pranzetti: So we call it a jar, the potential that includes basically they disappear destruction contained me Tanya. The composition of GR 308 00:42:52,020 --> 00:43:07,530 Daniele Pranzetti: And this is press the one in fact that best the momentum densities conjugated to the induce metric. So it's eliminating to rewrite this in the first hundred variables to show or the fundamental nature of this potential which takes except listen for what they are not good now have this 309 00:43:08,610 --> 00:43:15,660 Daniele Pranzetti: Mental entity is the momentum charge. I was showing you before the API, which is this for momentum aspect. 310 00:43:16,200 --> 00:43:27,300 Daniele Pranzetti: And it's related again to them to the portion of the adventure entangled. This relates portion of the actual better connection and the country barber is the, the owner of the math, which is there, the friend field. 311 00:43:29,040 --> 00:43:38,460 Daniele Pranzetti: And in fact, one can think of these as the reducing what potential caption the bat canonical degrees of freedom, which are common to end formulation GR 312 00:43:39,210 --> 00:43:47,070 Daniele Pranzetti: And starting from this combo piece. Any other formulation of gravity can be understood as being built basically from this job potential plus some band director 313 00:43:47,880 --> 00:43:55,350 Daniele Pranzetti: And we will speak to show this in the center of gravity for a reason. But this can be this short facing the Iceland Hebrew formulation and and formulation 314 00:43:56,370 --> 00:44:05,460 Daniele Pranzetti: And then in the absence of matter. So the destruction. I'm showing here is that we tend to have any formulation can read as the buck job class some boundary piece. 315 00:44:06,660 --> 00:44:20,580 Daniele Pranzetti: Then of course in Absalom market, especially for more efficient takes the form of the conservation equations for the momentum density. So we see that this conservation law of this momentum. It's just the first order. If you want equivalent or what happens metric, grab the case. 316 00:44:22,290 --> 00:44:23,730 Daniele Pranzetti: And 317 00:44:25,140 --> 00:44:31,800 Daniele Pranzetti: And then they so we can write, basically, especially from a threesome as conservation of this for momentum aspect now. 318 00:44:32,820 --> 00:44:39,450 Daniele Pranzetti: If you look at them. If any charges then Lucy did the look at tangent. He feels and 319 00:44:40,140 --> 00:44:46,140 Daniele Pranzetti: We do is just usually we contract this entity structure than the derivative alone. The vector feel excited, which is tangent 320 00:44:46,860 --> 00:44:56,760 Daniele Pranzetti: And what went up with some Italian generator which is about peace and the boundary piece. So the but pieces just, again, it's this may have vector constraint of canonical GR in the boundary piece is 321 00:44:57,420 --> 00:45:10,800 Daniele Pranzetti: Again, this is exactly this charge. I was showing you before that you issue right in the first order from is exactly the same quantity which is nothing has the brown your charge. So this brown. Your child is this which are meant to charge. I was 322 00:45:11,610 --> 00:45:17,970 Daniele Pranzetti: I was talking about earlier. And this shows as the common piece of the boundaries in the algebra graduates basic game by disintegrated presentation. 323 00:45:18,420 --> 00:45:28,080 Daniele Pranzetti: Of the different are facing tangent to the surface. So this is a piece which is common to any formulation which comes from this data jr component of their potential. 324 00:45:29,670 --> 00:45:31,800 Daniele Pranzetti: Now if we go to the tender from nation. 325 00:45:34,050 --> 00:45:41,520 Daniele Pranzetti: So we introduce a keyframe field and Lawrence connection which our country as independent Bibles, then the buck. 326 00:45:42,480 --> 00:45:52,020 Daniele Pranzetti: So this is the ice and Katana grandjean be field contains the two parts is the usual pieces star emoji. And then there is a 327 00:45:52,950 --> 00:46:01,770 Daniele Pranzetti: Very meets the perimeter component. And so the synthetic potential is given by this. But expression here in terms of be an omega 328 00:46:02,070 --> 00:46:09,510 Daniele Pranzetti: But now if we produce it will care for free plus one. The composition of all the geometrical quantities that appear in data gravity. 329 00:46:09,780 --> 00:46:16,260 Daniele Pranzetti: We can show that basically this potential can be become post again in the bud piece which is exactly the data jar that 330 00:46:16,770 --> 00:46:23,370 Daniele Pranzetti: Was Australia before. Then they said peace which vanish if you go and share the gospel as this increasing constraint. 331 00:46:24,030 --> 00:46:34,200 Daniele Pranzetti: There is another piece which is just the population, which doesn't affect the synthetic form which is given talking to her, and then there is the boundary component of ice and Captain formulation which I'm not going to show you 332 00:46:35,550 --> 00:46:37,350 Daniele Pranzetti: Explicitly I'm going to do in the next slide. 333 00:46:38,970 --> 00:46:46,350 Daniele Pranzetti: This is just to really show the structure of the synthetic potential of this I think enough formulation which follows the same pattern I was mentioning 334 00:46:47,610 --> 00:47:05,490 Daniele Pranzetti: And then they saw the lot the different charities are as before. Nothing changes the new thing is now that we have known when she Lawrence charges for CC to launch transformations and you see that basically the boundary charges are given by the boundary be field now. 335 00:47:06,540 --> 00:47:11,310 Daniele Pranzetti: And this contains two pieces. There is a boost part with in terms of this 336 00:47:11,880 --> 00:47:22,290 Daniele Pranzetti: Big which from shell of the simplicity takes this form here. And then there is the rotation part of the usual Titian part to that I was showing you on the time each case. So this for 337 00:47:23,130 --> 00:47:32,400 Daniele Pranzetti: Now just, I'm not going to talk about the formulation, but there is an expression of the synthetic addition to that gravity in the work of the morning 338 00:47:33,780 --> 00:47:47,130 Daniele Pranzetti: And the poly and I will if you want to talk about there. I would suggest that we do at the end of the talk because it's not really going to be discussing longer between the rest of their of 339 00:47:48,150 --> 00:47:54,270 Daniele Pranzetti: The talk. But again, when can show that this structure of a bad piece of the job, plus a brand new piece can be recorded. 340 00:47:55,860 --> 00:48:04,170 simone: Right to just do in the case of Anthony, but also there is a boundary term, but it is right. He's just that is different from day one. 341 00:48:05,700 --> 00:48:06,210 Daniele Pranzetti: Yes. 342 00:48:06,510 --> 00:48:07,320 simone: Sorry about the noise. 343 00:48:07,680 --> 00:48:08,250 Yeah. 344 00:48:09,360 --> 00:48:14,580 lsmolin: So the this Lorenz charge of vanishing is equivalent to the boundaries and 345 00:48:15,840 --> 00:48:18,420 lsmolin: Constraints boundary simplicity constraint. 346 00:48:19,710 --> 00:48:21,450 Daniele Pranzetti: Yes. Once you have detriments 347 00:48:22,140 --> 00:48:27,300 lsmolin: Yeah. So what's the interpretation of the charges the failure of the boundaries in place, you 348 00:48:28,440 --> 00:48:45,450 Daniele Pranzetti: Know it's so easy. That's what I was trying to say the first area is that you can see recover engage in violence in the sense that you can set the gate charges zero by you're still left with symmetry charges which are just the one given now, but the Edge mode. 349 00:48:46,530 --> 00:48:55,800 Daniele Pranzetti: Component. So you have the 3D representation of the boundaries in the algebra given by the fact that you have included edge modes which 350 00:48:56,880 --> 00:49:02,310 Daniele Pranzetti: Apulia independent from this pullback have resolved the boundary value of the field coming from the bike. 351 00:49:05,400 --> 00:49:06,750 Daniele Pranzetti: Maybe this is going to be clear. 352 00:49:07,920 --> 00:49:17,280 Daniele Pranzetti: In a moment, if one include the Edge mode for the Lawrence second largest but yeah the charges are basically 353 00:49:20,010 --> 00:49:27,210 Daniele Pranzetti: Is there again, but the Edge Mode which corresponds to if you want killing this Lawrence charge here. 354 00:49:29,760 --> 00:49:35,280 Abhay Ashtekar: So is a point that it's only on shelf that the edge more so related to sigma right 355 00:49:35,550 --> 00:49:38,970 Abhay Ashtekar: Yes, yes. And so therefore, but here you are not on shelf. 356 00:49:39,210 --> 00:49:39,930 Daniele Pranzetti: Know, yeah. 357 00:49:40,260 --> 00:49:43,290 Daniele Pranzetti: Yeah, I've included the Edge Mode yet yeah but 358 00:49:43,320 --> 00:49:48,150 Abhay Ashtekar: And you are not on shelves. So there is more independent determined by what is happening, the ball. 359 00:49:48,210 --> 00:49:49,050 Daniele Pranzetti: Yeah. Yes. 360 00:49:49,080 --> 00:49:57,930 Abhay Ashtekar: Except for and therefore you can be God as the bulk rotations as gauge, but the boundary rotations, not as case is that the pork. 361 00:49:58,200 --> 00:50:00,900 Daniele Pranzetti: Yes, absolutely. Yes, that's a point. Okay, thank you. 362 00:50:02,730 --> 00:50:05,010 Daniele Pranzetti: Okay, so now we can add electric which months. 363 00:50:07,980 --> 00:50:17,160 Daniele Pranzetti: And then we can follow the same strategies we didn't have the case of the time, engage and we can resort to violence and Lawrence invites by extending wonderful space. And so the edge months now. Are these 364 00:50:18,390 --> 00:50:32,910 Daniele Pranzetti: Fields here, there is the this big. EI. You notice I'm using different font exactly to stress the fact that these are pure independence on the boundary from the back fields these internal normal nine. Then there is the frame field. 365 00:50:33,990 --> 00:50:44,190 Daniele Pranzetti: And these are 16 degrees of freedom. And this is the boundary suppression of the synthetic potential that I didn't show you before now here use BF 366 00:50:44,610 --> 00:50:59,730 Daniele Pranzetti: To set you stress the fact that this big AI is not a priority related to it doesn't, it's not as pressing in terms of the of the frame field. It's a. These are independent fields to begin with and in n 367 00:51:01,980 --> 00:51:03,570 Daniele Pranzetti: So if we want now to 368 00:51:04,590 --> 00:51:13,710 Daniele Pranzetti: Record the gallery space. We have to impose extra constraint. And then there's the first set of constraints which is killing magical which are given by the fact that the new ization 369 00:51:14,460 --> 00:51:21,090 Daniele Pranzetti: Of this internal normal is speaks to minus one and then that basically the pulled back of the normal on the surface vanishes. 370 00:51:21,960 --> 00:51:31,140 Daniele Pranzetti: So these are the main constraint and if you use the person brackets, including this potential here to complete the algebra this constraint, you realize that the first piece here is first class. 371 00:51:31,410 --> 00:51:37,920 Daniele Pranzetti: And then this n equals zero is a second class component of this kinematic constraint. So what we can do then is to 372 00:51:39,330 --> 00:51:49,140 Daniele Pranzetti: derive a complete set of direct observable the commute with these constraints. And this basically give us 12 observable. It's the commutes with these constraints. 373 00:51:49,620 --> 00:52:03,570 Daniele Pranzetti: And these attributes are these the normal which is three degrees of field and they said boosts operator is bi, which is can be reading them. So the region of fields in this form. And then there is a tangential frame which is this ETF there which 374 00:52:05,040 --> 00:52:08,250 Daniele Pranzetti: Also is expressed in terms of the regional variables. 375 00:52:09,510 --> 00:52:16,140 Daniele Pranzetti: In this form and you can show that this free observable this preset observable now commute. 376 00:52:17,370 --> 00:52:26,400 Daniele Pranzetti: With the with this constraints with any magical constraints. So these are really acceptable in this, in the sense that they they go commit with this clinic module constraints and a parameter price. 377 00:52:26,760 --> 00:52:29,790 Daniele Pranzetti: They face based on Shelby for one of these constraints. 378 00:52:30,180 --> 00:52:42,930 Daniele Pranzetti: And particularly seated moose operator is conduit to this internal normal, why not required to because they're also an automation for some brackets. But as this awesome ragged, we've been phenomenal and day to day or to satisfy the analog of there. 379 00:52:44,070 --> 00:52:47,220 Daniele Pranzetti: Was some brackets for the boundary frame that I was showing you before. 380 00:52:48,420 --> 00:52:59,550 simone: Sorry, these are capital E. Yes, me, just the unit normal time like unit normal to the surface. So inside 381 00:53:00,840 --> 00:53:05,190 simone: Sigma engines piece, the sigma the 3D cushy ever surface. 382 00:53:07,050 --> 00:53:20,280 Daniele Pranzetti: This this country here a purity is independent on any of the structure when you go and share of the simply single string is because basically the flux discovery. 383 00:53:21,390 --> 00:53:23,280 Daniele Pranzetti: Is I'm going to show you, they're 384 00:53:23,340 --> 00:53:25,260 simone: Not nothing depends on the 385 00:53:25,710 --> 00:53:33,600 simone: eyeballs on the normal to s that Nandi nothing depends on the normal that that our minds as inside the see 386 00:53:34,200 --> 00:53:42,480 Daniele Pranzetti: A purity enn so we have n which is the one of the normals, the sort of internal normal and he is independent on and take the 387 00:53:43,500 --> 00:53:44,550 Daniele Pranzetti: Conjugate to each other. 388 00:53:45,180 --> 00:53:47,640 simone: Right. But this is only the second normal to us. 389 00:53:48,060 --> 00:53:51,210 Marc Geiller: Yeah, two minutes, asking if the second number two is it 390 00:53:52,290 --> 00:53:56,070 simone: Should be just the second number two is, if I remember correctly. 391 00:53:56,160 --> 00:53:58,140 Laurent Freidel: No, no, it will come. It will come there. 392 00:53:59,520 --> 00:54:01,470 Laurent Freidel: Is no, wait a minute. 393 00:54:02,010 --> 00:54:11,910 Daniele Pranzetti: Yeah, I mean, that what. Yeah, that would be a diff mean something which is related to it, but it's not it's not really that I will, I will show you in a second what it is just one side. OK. 394 00:54:13,890 --> 00:54:15,750 Daniele Pranzetti: OK, so now 395 00:54:17,640 --> 00:54:25,170 Daniele Pranzetti: The information about the tangential frame can be expressed in terms of speed operator. So is this this si 396 00:54:26,700 --> 00:54:30,630 Daniele Pranzetti: Simoni that it's really what the second moment is and 397 00:54:32,610 --> 00:54:40,380 Daniele Pranzetti: Actually mentioned engine tangential to all the information in this at that can be encoded that we're almost for us. We will see chemical in this 398 00:54:41,670 --> 00:54:48,180 Daniele Pranzetti: New quantities. This has been operator and there is a tangential metric and the true or not. They are not independent. 399 00:54:48,540 --> 00:54:56,100 Daniele Pranzetti: In the sense that there is a geometrical relation between these two that relates the su casa me with the determinant of this search bar. 400 00:54:56,880 --> 00:55:01,170 Daniele Pranzetti: Of these, the metric here which you've seen a second satisfied etc symmetry. 401 00:55:01,830 --> 00:55:08,280 Daniele Pranzetti: But the spin density generates unless you truly algebra, which preserves the internal normal. So this is the, these are the brackets. 402 00:55:08,550 --> 00:55:23,520 Daniele Pranzetti: And then one can show that the such large enterprise generated by this isn't a surcharge are generated by this kind of method with me, which I give you here. So this really is a relation between the switch accosted me, and such lot Casimir come from this observer boats. Yeah. 403 00:55:26,040 --> 00:55:27,210 Daniele Pranzetti: And 404 00:55:28,320 --> 00:55:39,360 Daniele Pranzetti: And the medical be of course also commutes with the generators. Big sigh Oh, the surgeon generators that I introduced before. So there is 405 00:55:40,530 --> 00:55:47,280 Daniele Pranzetti: This balance equations. And now what I'm going to do is finally to introduce the funk array. 406 00:55:47,730 --> 00:55:54,600 Daniele Pranzetti: So, one can see that, basically, if we introduce the starter on the moment and generators JJ, which are built from the other 407 00:55:55,200 --> 00:56:11,190 Daniele Pranzetti: Variables to introduce a five day boost the internal normal and the spin. So the first part can be understood as the angular momentum. The second part is the spin, then we see that this generator satisfy, together with the with the internal normal in algebra, which is upon carry algebra. 408 00:56:12,270 --> 00:56:16,110 Daniele Pranzetti: So the first line here is basically the such as see sector. 409 00:56:17,340 --> 00:56:23,310 Daniele Pranzetti: Which generates large transformation. The boundary space. And these are related, basically, to the boundary cows law. 410 00:56:29,070 --> 00:56:49,110 Daniele Pranzetti: Basically by the button. You see that is generated, Jr. But if the back of the field by the boundary gap slow. So this is what I was, was asked before. And so when you post these the charges vanish. But this now you have the SF DC symmetry generated by this Jay Jay Jay 411 00:56:50,760 --> 00:56:51,090 Daniele Pranzetti: And 412 00:56:52,590 --> 00:56:53,220 Daniele Pranzetti: And now. 413 00:56:54,270 --> 00:57:04,380 Daniele Pranzetti: You see that the balance equation or basically what it does that actually before release day one, Christina Casimir to the boundary medic determinant 414 00:57:05,430 --> 00:57:19,410 Daniele Pranzetti: So what this equation means is that, then the element is given by this elemental conquering and spin and is therefore Lawrence importance quantity and this is really due to the fact that the normal now is has become the angle. 415 00:57:21,600 --> 00:57:30,060 alejandroperez: That nearly one question in the previous slide, the equation you showed looks similar to something we had with the 416 00:57:31,260 --> 00:57:32,790 alejandroperez: Long in the paper. 417 00:57:32,880 --> 00:57:34,680 alejandroperez: quandary that the corner, what 418 00:57:35,430 --> 00:57:36,690 Daniele Pranzetti: You're the first reference here. 419 00:57:39,060 --> 00:57:39,390 Daniele Pranzetti: It's 420 00:57:40,350 --> 00:57:41,040 alejandroperez: The same thing 421 00:57:41,430 --> 00:57:46,320 Daniele Pranzetti: It's, it's the, what was the tango version of this basically 422 00:57:47,280 --> 00:57:48,060 alejandroperez: I see. Okay. 423 00:57:48,150 --> 00:57:50,610 Daniele Pranzetti: This image of is just we all the time. He 424 00:57:51,390 --> 00:57:52,980 alejandroperez: Okay, thank you. Yeah. 425 00:57:53,910 --> 00:57:59,190 Daniele Pranzetti: Yeah, I mean this this is this essential as a long history. Somehow it just that. 426 00:58:01,110 --> 00:58:17,580 Daniele Pranzetti: It was never really taken seriously, to a certain extent what we're, what we're seeing here is that it's a fundamental observable in order to reconstruct the tangential frame is not something that you can just, you know, kill innocuously 427 00:58:19,800 --> 00:58:20,160 Daniele Pranzetti: And 428 00:58:21,390 --> 00:58:22,260 Daniele Pranzetti: So we see that 429 00:58:23,880 --> 00:58:29,040 Daniele Pranzetti: The, the surface element is a learning environment and 430 00:58:30,060 --> 00:58:38,640 Daniele Pranzetti: What's very nice consistency check is the fact that as we can understand this area man autos and etc. 431 00:58:39,180 --> 00:58:51,870 Daniele Pranzetti: Casimir, then it's not obvious that you will have a discrete representation for the for the spectrum, but the fact that they're basically that the surface is based like selects the discrete a search or presentation. 432 00:58:52,470 --> 00:59:01,440 Daniele Pranzetti: So there is this compatibility between the sweetness Lawrence inviting that shows up in this balance equation and between essential are passing MDA on careers Pincus me 433 00:59:02,220 --> 00:59:11,430 Daniele Pranzetti: Now if you want to have a better understanding of this elemental punk reality rap, we can try to introduce some particle like parameter ization of the algebra. 434 00:59:11,760 --> 00:59:23,280 Daniele Pranzetti: In terms of those two letters, where we have this excited, which is a particular position, we have the momentum bi the particle moment and then we have some internal degrees of freedom, which is a nice pair of oscillators. 435 00:59:24,960 --> 00:59:37,950 Daniele Pranzetti: And then the total the moment is in Mario under translation generated by this generators PA defined like this and the p square and this this generators, Jenna. 436 00:59:38,580 --> 00:59:48,810 Daniele Pranzetti: Define for the ice and pre algebra. So now we can we can fix this ambiguity, Issue one by choosing going to the nursery where we said to equal to zero and then 437 00:59:49,920 --> 00:59:54,120 Daniele Pranzetti: We see that this condition basic breaks, they seem to group them to center. 438 00:59:54,570 --> 01:00:03,120 Daniele Pranzetti: And then the dramatic dramatically. They seem to break in Mexico ensures that the moment our normal to the sphere and additional terms often position of discuss 439 01:00:03,780 --> 01:00:13,680 Daniele Pranzetti: Initial from constraint, what we see is basically said the flax corresponds to a relativistic positional potato and the frame correspond to the spinner simulator. 440 01:00:14,460 --> 01:00:25,560 Daniele Pranzetti: So, and, as I was saying before, is the is the momentum and this this risk of the mass which is an interesting to prediction, which basically if you introduce the party basket vector 441 01:00:26,220 --> 01:00:39,690 Daniele Pranzetti: You can see Bessie from the special of the Casimir the second customer that the mass of this one career, a particle particle is really related to the mid see parameter 442 01:00:41,160 --> 01:00:41,550 Daniele Pranzetti: So, 443 01:00:42,690 --> 01:00:44,190 Daniele Pranzetti: What this is saying is that basically 444 01:00:46,290 --> 01:00:55,830 Daniele Pranzetti: once a semester just interpretation, the spinner to link as a particle of quantum space which cares. It's been s and the mass given by the Missy parameter 445 01:00:57,090 --> 01:01:07,260 Daniele Pranzetti: Or then one quote something for instance of the gamma zero limit and then you see in this picture. The gamma gluten to limit Betsy corresponds to the medical face corresponds to the merciless 446 01:01:08,640 --> 01:01:19,560 Daniele Pranzetti: Limit of the select from this elementary punk and metal punk or a point of view. So this is just to give maybe a bit more of a physical interpretation of this boundary variables here. 447 01:01:21,390 --> 01:01:29,550 Daniele Pranzetti: OK, now there is a second set of some pieces, which is really where we're interested in is the boundaries and physical strength and 448 01:01:30,720 --> 01:01:37,560 Daniele Pranzetti: This is the best relate the booster operator to this innovator. Now this is these are free. So conditions because there is this 449 01:01:38,610 --> 01:01:49,590 Daniele Pranzetti: Wanting the medical relation satisfy that only few of these four components are independent and one can show using the space that we introduced that there is they don't be satisfied is algebra. 450 01:01:50,430 --> 01:02:01,380 Daniele Pranzetti: From the continue or we can see that this is the algebra dissatisfied. We're not is that this the first piece here is that this is different from the discrete touch with one of things from disquisition producing the phones. 451 01:02:02,400 --> 01:02:06,690 Daniele Pranzetti: But again, these other shows that basically these constraints are second class and 452 01:02:10,560 --> 01:02:14,820 Daniele Pranzetti: So what this does basically he's constraint killed four degrees of freedom because 453 01:02:15,450 --> 01:02:24,180 Daniele Pranzetti: Since they are free constrain means that one has to be first class. In short, there has to be second class. So they call they can choose degrees of freedom. And when that Dan is with 800 year cups. 454 01:02:24,990 --> 01:02:29,490 Daniele Pranzetti: So these are the ones that now we want to recover eventually Lisa understand what are the state, you know, 455 01:02:29,490 --> 01:02:29,850 Great. 456 01:02:31,020 --> 01:02:38,730 Muxin Han: Hi done yet. So about the previous life. So if you include cosmological constant does this outer bark at the form somehow 457 01:02:43,980 --> 01:02:47,100 Daniele Pranzetti: Possibly, yes. We haven't really looked into that. 458 01:02:49,230 --> 01:02:50,730 Daniele Pranzetti: But that's possible. 459 01:02:52,080 --> 01:02:54,150 Daniele Pranzetti: That. Okay. Okay. Yeah. 460 01:02:55,170 --> 01:02:55,440 Muxin Han: Yeah. 461 01:02:55,980 --> 01:02:57,450 lsmolin: That sounds really interesting 462 01:03:00,660 --> 01:03:01,470 Daniele Pranzetti: Right, so 463 01:03:04,080 --> 01:03:06,750 Daniele Pranzetti: Okay, now we can so we can use. Now, the set of 464 01:03:08,460 --> 01:03:13,350 Daniele Pranzetti: Fields and I si N et di it's not to talk on basis. So you see this is 465 01:03:14,760 --> 01:03:28,440 Daniele Pranzetti: Someone was asking this aside plays the role of this economic one. And we can decompose this constraint and see that there is a second class pair which are given by the tangential part if you want of the constraints and they're satisfied this algebra here. 466 01:03:31,440 --> 01:03:46,950 Daniele Pranzetti: And then and now we can isolate the first class term and which commute strongly with the second task constraint and turns out the best. It's a combination of two possible candidates, which are see square and see the. So today, the pistons are the potential to us. And this is where and 467 01:03:48,390 --> 01:03:49,140 Daniele Pranzetti: In 468 01:03:50,250 --> 01:03:55,290 Daniele Pranzetti: One can also see the basically this first class constraint is a function of the central seekers image only 469 01:03:56,310 --> 01:04:03,540 Daniele Pranzetti: Which is going to be useful. Eventually, for the implementation of a string. So now this expression here is the first gospel singer, which basically 470 01:04:04,320 --> 01:04:12,210 Daniele Pranzetti: Corresponds to the content version of the district diagonal simplicity constraint, as it was a returning recently in the paper of Canon Law and smaller. 471 01:04:12,600 --> 01:04:22,350 Daniele Pranzetti: There should be some special is introduced us the Lawrence inviting part of the Indian and the speed, simplicity can see which we pleased, they have they have the young CPC constraint in the 472 01:04:23,520 --> 01:04:31,890 Daniele Pranzetti: FK piano model. We're over. Speaking of this in physical symptoms of first class second class was also done. For instance, in the spirit my work done. 473 01:04:32,490 --> 01:04:34,710 Daniele Pranzetti: In this sprint from formulation 474 01:04:35,430 --> 01:04:47,820 Daniele Pranzetti: Let me just point out that, however, the first place where this expression appear is in this paper or whether and then yell already. He doesn't true so way before the new models. In fact, they, they were trying to recover the Berkeley. 475 01:04:48,240 --> 01:04:57,660 Daniele Pranzetti: Berkeley quantum constraints on the representation in the case in which one include includes the music or music to be affection and I think it's quite interested in this quote 476 01:04:58,980 --> 01:04:59,910 Daniele Pranzetti: What they say that 477 01:05:01,050 --> 01:05:01,830 Daniele Pranzetti: One should be 478 01:05:02,970 --> 01:05:12,270 Daniele Pranzetti: It's not easy to construction system. For example, using non simple presentation but this should be investigated. In fact, a few years later, we know what the 479 01:05:12,990 --> 01:05:24,570 Daniele Pranzetti: History for the path. But anyway, so this first class components. It's not new. It's a as a PA before you need to. But the second class, especially here it's I think it's 480 01:05:25,650 --> 01:05:26,400 Daniele Pranzetti: It's quite a new 481 01:05:27,600 --> 01:05:28,800 Daniele Pranzetti: Especially that we found. 482 01:05:30,180 --> 01:05:32,520 Daniele Pranzetti: Now the Cubs ever boats. 483 01:05:33,570 --> 01:05:35,970 Daniele Pranzetti: So it's best to me to see that. 484 01:05:40,800 --> 01:05:46,740 Daniele Pranzetti: The JJ the generators of the Lawrence decimation they are all basically the old commute with 485 01:05:48,300 --> 01:05:57,780 Daniele Pranzetti: With this kinematic constraint and with the same physical same retreat in terms of first class second class piece, which means basically they taught on the momentum. 486 01:05:58,590 --> 01:06:09,540 Daniele Pranzetti: Form 16 strong Dirac upset boats and again this is affect the Lauren symmetry reflection inside the learning team is preserved by the imposition the simplistic constraint and they can the magical constraint. 487 01:06:11,370 --> 01:06:22,590 Daniele Pranzetti: And however this is no longer true. If we look at the boundary medical appointments. They don't sound. The commutes with the second guessing PCT and to fix this one can for the commerce strategy in 488 01:06:23,490 --> 01:06:30,330 Daniele Pranzetti: In order to deal with segment has constraints in form which is basically replaced it. The second class component of this MPC will still be the Master Splinter 489 01:06:30,960 --> 01:06:38,250 Daniele Pranzetti: And you can continue then basic. The second class nature of this constraint. It's affected by the fact that the drug embed doesn't appear in respect of the master constraint. 490 01:06:38,790 --> 01:06:49,020 Daniele Pranzetti: And we can position the casino in a month to selecting mean we're getting value instead. But we, we've seen a moment that I mean there is this approaches vehicle with some subtleties, but 491 01:06:50,250 --> 01:06:59,520 Daniele Pranzetti: For the moment, let's just follow the path and replace the master conspiracy. The second class with the massive constraint and this is the expression that we find 492 01:07:00,450 --> 01:07:11,550 Daniele Pranzetti: And it can be checked that this expression here now is such that the boundary medical mute strongly with with the master constraint. So they ought to be free tangential medical points are 493 01:07:11,880 --> 01:07:26,880 Daniele Pranzetti: The represent the three remaining vehicles circles. So what we did then is revealed at the boundaries in the group is of ground in the teller formulation is given by a citrusy cross, etc. Now there is 494 01:07:27,990 --> 01:07:34,560 Daniele Pranzetti: A downward partner seeming to breaking that has been going on. So first we started with this chart cross the Heisenberg 495 01:07:35,400 --> 01:07:45,480 Daniele Pranzetti: Algebra and then posting the initial friend constraints basically breaks the same three down to set to our and then the same thing happens for the other 496 01:07:46,200 --> 01:07:56,610 Daniele Pranzetti: Click on the CPC was saying, we start with a concrete group and imposing the database constraint breaks it down to a central see so that the final symmetry algebra. It's a central processor 497 01:07:59,670 --> 01:08:06,090 Daniele Pranzetti: Now let me let's grind them more dramatic insight into the search bar sector. 498 01:08:06,540 --> 01:08:17,340 Daniele Pranzetti: Now, what we saw is that the physical boundaries basis parameters financial troubles. However, I was mentioning that not all of them are independent. In particular, there is a geometrical bands equation, which relates the pancreas been 499 01:08:19,320 --> 01:08:32,340 Daniele Pranzetti: To the asset to our customers. So what this means is that we still need one more valuable basically to reconstruct the boundary frame and this Bible is given by an angle which represents the information in the frame that is not capturing SI and into a big 500 01:08:33,390 --> 01:08:37,200 Daniele Pranzetti: One can check the sap basically left in by by just permission. 501 01:08:38,790 --> 01:08:51,060 Daniele Pranzetti: Parameters, but this angle. So we introduced this one here. So if you do this information, you can see that these companies are left environment, in particular, one can show that this angle is contribute to the area and 502 01:08:52,320 --> 01:09:07,290 Daniele Pranzetti: In fact, so this condition relational of tea, then the reform shows the best Tita is the analog of the priests angle enters the definition of the twisted geometry and this angle is necessary in order to reconstruct along along the edge relating to frames. 503 01:09:08,370 --> 01:09:22,080 Daniele Pranzetti: On the two sites. So you have two premises to the triangle shaped by Twitter data in order to reconstruct the Delano me that basic release these two frames you need this angle. This was shown by someone around 504 01:09:23,430 --> 01:09:24,990 Daniele Pranzetti: And this is the job description. 505 01:09:27,570 --> 01:09:31,230 Daniele Pranzetti: Of geometry. So, the, the joint is the description 506 01:09:32,460 --> 01:09:43,410 Daniele Pranzetti: Of discrete geometries associated can manifest based of gravity. And in general, the metric is this contains across the triangle shaped by the edge deployed and 507 01:09:45,150 --> 01:09:49,860 Daniele Pranzetti: Basically basin etc transformation which is needed to match the geometry in the two triangles. 508 01:09:50,490 --> 01:09:54,540 Daniele Pranzetti: And the simple way to see this. For instance, if to reduce the coordinate system that covers the 509 01:09:54,900 --> 01:10:09,600 Daniele Pranzetti: Shooter Phaedra bombing the training will face and then just for Michigan be in this to this linear transformation of coordinates. Basically the sensor condition three angle on one side. So from the conditions for angle to the other side and then 510 01:10:10,950 --> 01:10:27,750 Daniele Pranzetti: The boundary metric basically is exactly at this generators. So it's the generators of this ship matching transformation that codifies in the continuum. This information about the connection triangulation on the edge of the graph board is to drive downloads. 511 01:10:28,770 --> 01:10:35,850 Daniele Pranzetti: So also an interesting quote at the end of this was this assault charges from issuer shown in this nice paper here. 512 01:10:36,540 --> 01:10:48,150 Daniele Pranzetti: And the quote there at the end of the paper was that there's a reason for this increase equal string to suppress twisting and fail. We're seeing that this thing is absolutely compatible with the with the simplicity constraints effect. 513 01:10:49,590 --> 01:10:52,740 Daniele Pranzetti: Is necessary to reconstruct information a tangent frame. 514 01:10:54,600 --> 01:10:55,440 Daniele Pranzetti: And notes, let me 515 01:10:57,090 --> 01:11:02,850 Daniele Pranzetti: Point out that this church quality defines a complex structure on the surface, which is very important. In fact, 516 01:11:05,970 --> 01:11:10,920 Daniele Pranzetti: This established basically the default source the archdiocese compared with the person structure. 517 01:11:11,190 --> 01:11:24,330 Daniele Pranzetti: And this is based in Portland renting position or second class constraint, as I'm going to share in a moment. My more Jeff in this project of the originator of this area affected the air is a generic have this opportunity can have important implications of quantum theory. 518 01:11:25,980 --> 01:11:31,230 Abhay Ashtekar: I just have a quick question. I mean, until the last slide, you're always in the continuum and 519 01:11:31,260 --> 01:11:38,940 Abhay Ashtekar: Gary. Oh, yes. Now you're making this transition in this this diagram that you're drawing about the twist angle and so on for some time. 520 01:11:39,630 --> 01:11:41,640 Daniele Pranzetti: Before. Now I'm trying to 521 01:11:42,750 --> 01:11:50,820 Daniele Pranzetti: To show that this continuous variables are continue analog of quantities that have been produced in the literature. 522 01:11:51,870 --> 01:11:57,390 Abhay Ashtekar: Good. Okay. Thank you. Bye bye. But yet, you're not going to be working with a with 523 01:11:59,280 --> 01:12:01,050 Abhay Ashtekar: Always going to be working in the continuum is that 524 01:12:01,050 --> 01:12:02,370 Daniele Pranzetti: Right. Yes. Is 525 01:12:02,610 --> 01:12:03,270 This just 526 01:12:04,890 --> 01:12:12,360 Daniele Pranzetti: To clarify some passive existing the twisted jaunty about the compatibility between the twisty angle and this NPC constraint. 527 01:12:13,950 --> 01:12:14,580 Abhay Ashtekar: And 528 01:12:14,670 --> 01:12:15,120 Abhay Ashtekar: Okay. 529 01:12:15,150 --> 01:12:18,600 Daniele Pranzetti: Thanks. So yeah, OK, so 530 01:12:20,040 --> 01:12:25,440 Daniele Pranzetti: Just me summarize what we saw is that the the edge of astronomy go observe is generated by this 531 01:12:25,950 --> 01:12:34,140 Daniele Pranzetti: JJ and the Qb. And for the boundaries in algebra is different formulations game at the essential see processor to are you today. 532 01:12:35,010 --> 01:12:47,790 Daniele Pranzetti: Eric observable and the boundary space. And here is a big roadmap of the path, but I think I'm going to need, so I'm not gonna go through this. Let me just now the last part of the talk. It's a body position of the 533 01:12:48,930 --> 01:12:49,920 Daniele Pranzetti: Simplicity was strange. 534 01:12:51,090 --> 01:12:57,240 Daniele Pranzetti: So a way to pro feminism has consumed one to level is basically still rely on the Gutenberg prescription 535 01:12:57,600 --> 01:13:04,050 Daniele Pranzetti: But this requires a specific choice of a complex structure on the face base, which has to be compared to the clustering algebra. 536 01:13:04,590 --> 01:13:19,830 Daniele Pranzetti: Now, as we've seen before. This has been provided this article ID is available, do they affect the frame field on the boundary space is private message that the frame. Feel the benefit space and then. So the strategy is to impose second class simplicity 537 01:13:21,030 --> 01:13:33,930 Daniele Pranzetti: Two steps. First, we use the compatibility of the door with a bracket to establish that we can basically we can define your market constraints, the pluses and minus, such as they compete with each other. 538 01:13:34,560 --> 01:13:44,760 Daniele Pranzetti: And then we replace the second class constraints to do with the first class condition that c minus eight equals zero. Word. Now, this can be imposed strongly on 539 01:13:46,230 --> 01:13:46,980 The quantum level. 540 01:13:48,780 --> 01:13:50,520 Daniele Pranzetti: But, as was mentioned earlier. 541 01:13:51,600 --> 01:13:55,740 Daniele Pranzetti: It's often convenient to replace these conditions equals zero, with the master constraint. 542 01:13:56,490 --> 01:14:04,680 Daniele Pranzetti: Now the classical level. The two things are equivalent at the quantum level one has to be a bit careful because messy. What happens is that when you read the master constrain 543 01:14:05,010 --> 01:14:18,270 Daniele Pranzetti: You get this quote the same expression, but you also get an anomaly which takes everyone down here, but it doesn't matter. Exactly discretion is just, it's an anomaly, of course, to the the commentators now. 544 01:14:19,560 --> 01:14:20,130 Daniele Pranzetti: So, 545 01:14:21,150 --> 01:14:29,250 Daniele Pranzetti: If you post strongly ca zero c minus two equals zero, then you have this relation for the between the massive constraint anomaly on the steak. 546 01:14:30,630 --> 01:14:31,860 Daniele Pranzetti: And it's only 547 01:14:33,090 --> 01:14:40,680 Daniele Pranzetti: means basically only if the anomaly commutes with the this sometimes constraint that you can really 548 01:14:42,330 --> 01:14:53,280 Daniele Pranzetti: Identify the meaning and value of the master constraint with a good value of the anomaly evaluated on the state that they have analyzed both C minus na 549 01:14:53,910 --> 01:14:59,130 Daniele Pranzetti: And one can check that this is the case in the foreign debt financing that we wrote by basically 550 01:14:59,490 --> 01:15:07,890 Daniele Pranzetti: You can use a semi classical evaluation of the anomaly gives you this expression for the anomaly and then you can check that this anomaly commutes 551 01:15:08,280 --> 01:15:17,970 Daniele Pranzetti: Basic this weekly if you want with this emancipated enough because the mind is can be imposed strongly now. So if you can meet weekly with the the constraint. It's means that 552 01:15:19,500 --> 01:15:32,400 Daniele Pranzetti: You can say to zero this bracket. And so the the computer. Yes. So this is just a consistency check that the massive constraint approach can be is complete, it's consistent with the weekend position of the second tax constraints. 553 01:15:32,880 --> 01:15:39,000 Daniele Pranzetti: Okay, so let's find an important this constraints. First we need to admit the bundle space. 554 01:15:40,260 --> 01:15:45,480 Daniele Pranzetti: And what to do. So it's important to remember that the Lawrence algebra emerges from the elements of concrete algebra. 555 01:15:46,050 --> 01:15:53,160 Daniele Pranzetti: Once this is increasing constraints are introduced. So it's, it would be useful to introduce first upon carry algebra at the bunker representation 556 01:15:53,820 --> 01:16:06,180 Daniele Pranzetti: So introduce introduce me to your presentation where we live by the various of the customer and square which is the momentum square. It's minus one and then they disappear customer takes this label by this 557 01:16:07,440 --> 01:16:18,960 Daniele Pranzetti: half integer s now as usual can introduce ecumenical were to TI and define a kidney magical rotation generated in terms of it and then 558 01:16:20,700 --> 01:16:29,700 Daniele Pranzetti: It's important to keep in mind that the SI this paint the bookcase penis enjoy different from this kind of magical or generator. It's only when you go to the time engage that the choo. 559 01:16:30,930 --> 01:16:33,780 Daniele Pranzetti: Choo are the same. So basically, this means that 560 01:16:35,460 --> 01:16:37,950 Daniele Pranzetti: There is no germination between j and s 561 01:16:39,030 --> 01:16:45,180 Daniele Pranzetti: See the classical it's increasing constraint that restricts further than the fact that J squared will be bigger than a square but 562 01:16:46,290 --> 01:16:55,560 Daniele Pranzetti: And this is going to hold on to the quantum theory, but in Singapore to keep into account, it s NJ two separate one two numbers. So then what we can do is to 563 01:16:56,340 --> 01:17:05,700 Daniele Pranzetti: Introduce the cut down by basis which is adapted to the merge them this learning symmetry. And this is formed by a set of commuting emission generators that can all be diagonal is at the same time. 564 01:17:06,000 --> 01:17:20,460 Daniele Pranzetti: So using it for you so nice. And you can see that the set the set of generator approved by the checkpoint and Kerri Kasem is the true Lawrence Casimir screen cookies. And then there's the kingdom article spinner J squared and its component Jeffrey, so what what we have are basically 565 01:17:22,230 --> 01:17:31,440 Daniele Pranzetti: Five quantum numbers because Esquire, it's been fixed them and Swan with us. We have Brian K, which are labeled today. Lawrence Casimir and then we have Jay and m which 566 01:17:31,830 --> 01:17:50,550 Daniele Pranzetti: Corresponds to this magical spin quantum numbers and these are the the egg and values of this observable to. So now on this space, we can increase the constraint we start with the first class, which can be strongly and this gives us a tradition of right as a function of key. 567 01:17:52,020 --> 01:18:00,240 Daniele Pranzetti: Again, we have two branches, but only one. It's as the correct some classical limit. So it's the give us the usual erotically retardation. 568 01:18:00,780 --> 01:18:18,540 Daniele Pranzetti: And now we can impose the second class constraint. Again, we're looking for demand innovative the master constraint and by using this solution or plus we found before Bessie, one can see that the main minimum value is given by the condition that case will be equal to us. 569 01:18:20,100 --> 01:18:26,760 Daniele Pranzetti: So what this shows is that the physical vessel in order to solve some cross constraint. 570 01:18:32,280 --> 01:18:44,280 Daniele Pranzetti: We can we can label the physical space by to spin. There's the pancreas been s and economical spin j, which is fenestration just to be bigger than S and 571 01:18:45,600 --> 01:18:54,000 Daniele Pranzetti: Lauren cemetery is fully preserved or to the quantum level, we have a representation of the assets juicy algebra at the quantum level and then 572 01:18:55,440 --> 01:18:58,920 Daniele Pranzetti: This means the best at the quantum level this in physical restraints can be implemented. 573 01:18:59,310 --> 01:19:09,120 Daniele Pranzetti: By embed and embedding a bit later if you want the maps their presentation. So to see into the bunker representation which is if you wanted generalization of the many map. I will show you at the beginning. 574 01:19:11,160 --> 01:19:12,750 Daniele Pranzetti: Okay, so let me conclude 575 01:19:15,060 --> 01:19:20,700 Daniele Pranzetti: So we see basically the edge for formalism capture the nature of the local news feed on which are involved. 576 01:19:21,060 --> 01:19:29,220 Daniele Pranzetti: In the division and the scene of the systems in the subsystems. Now this process can be in the switcher brightly as the fusion of states associated with boundary symmetry algebra. 577 01:19:29,850 --> 01:19:36,810 Daniele Pranzetti: And this understanding Hopkins away to a new description on geometry where features of photographing economic approaches can be combined. 578 01:19:38,010 --> 01:19:47,310 Daniele Pranzetti: Now the country on it that we perform the same physical strain basically shows that the boundary symmetry group is the correct group which is generated by this 579 01:19:47,820 --> 01:19:57,180 Daniele Pranzetti: Lawrence and the moment that antenna normal n and before the imposition of the CPC constraints. Now, the presence of discernment upon k 580 01:19:58,320 --> 01:20:12,900 Daniele Pranzetti: Which is purely associated to the geometry. There's no matter that we introduced so far HERE. IT'S QUITE SURPRISING FEATURE OF THE CONSTRUCTION by sorts of their recent guy on this nice property with the with arriving in particular, we saw that 581 01:20:14,340 --> 01:20:29,910 Daniele Pranzetti: The time like direction becomes dynamical Bible, please. The momentum and gets routed by the Lord to traders and, most importantly, we saw that missing piece. He was only big the transitional subgroup of conquering but preserves the learnings in violence. 582 01:20:30,930 --> 01:20:35,130 Daniele Pranzetti: And this is compatible with a with a discrete specter of the Arabic 583 01:20:36,510 --> 01:20:39,630 Daniele Pranzetti: And the boundary symmetry algebra contains or two. This is such 584 01:20:41,070 --> 01:20:44,370 Daniele Pranzetti: A component which is necessary to reconstruct the tangential frame. 585 01:20:45,030 --> 01:20:53,340 Daniele Pranzetti: And this means the best. We need to look into numbers, North Korea constructed tangential frame operator is the pancreas DNS and there's a quantum shape if you want 586 01:20:54,060 --> 01:21:06,690 Daniele Pranzetti: Number, which corresponds to an integer. And that label states in reducing position or the presentation or central which I didn't really have the time to talk about this representation here, but it's a familiar episode number in the representation cetera 587 01:21:07,950 --> 01:21:25,020 Daniele Pranzetti: So basically showing how the suspended boundary algebra provides the continuum of structure which were introduced in recent geometry description and the imposition of this increasing constraints does not imply the position should match conditions. 588 01:21:26,130 --> 01:21:37,890 Daniele Pranzetti: And particular among many directions and now this offense this quantum numbers can play an important role in understanding for isn't the flatness problems in forms which has been a topic of 589 01:21:39,540 --> 01:21:54,840 Daniele Pranzetti: Edge that's generated a lot of activity and also this morning there was an Uber about this and we find that this understanding, could that could help solving the contrast between different approaches. Okay, thank you very much for listening, sorry for being so late. 590 01:22:11,850 --> 01:22:17,700 Abhay Ashtekar: I understand now the general philosophy from the point of view of going beyond kinematics. 591 01:22:18,120 --> 01:22:19,770 Abhay Ashtekar: Mm hmm. So 592 01:22:20,940 --> 01:22:23,070 Abhay Ashtekar: On slide 18 you had this 593 01:22:24,810 --> 01:22:38,250 Abhay Ashtekar: This fictitious particle description basically X MP and some internal degrees of freedom and so on so forth. So are you thinking the dynamics could be simple in terms of these political like variables or 594 01:22:39,000 --> 01:22:58,200 Daniele Pranzetti: Well, one thing that can simplify dynamics is the fact that the different field is available now in the sense that we don't have to rely on the Fluxus and the volume to describe the different field, but we have quantum numbers that allow us to reconstruct 595 01:22:58,860 --> 01:23:02,580 Daniele Pranzetti: Them in a more direct way and this could provide the 596 01:23:03,930 --> 01:23:07,470 Daniele Pranzetti: A new definition of time constraint. 597 01:23:09,540 --> 01:23:19,110 Abhay Ashtekar: Okay, but I mean at the moment that you sort of really have restricting yourself to the constraint. And so, I mean, you said there are observable that really kinematics. 598 01:23:20,160 --> 01:23:20,430 Daniele Pranzetti: Yes. 599 01:23:21,960 --> 01:23:31,560 Abhay Ashtekar: Okay, so, but is a viewpoint that you're still trying to get Hamiltonian constraint and then you will get a kind of a canonical theory or is this supposed to give you more. 600 01:23:33,180 --> 01:23:44,370 Abhay Ashtekar: I mean in economic theory in which then the fundamental thing would be just submission Hamiltonian constraint and it is not clear what time evolution means and so on so forth or 601 01:23:45,030 --> 01:23:45,570 Abhay Ashtekar: Yeah, I'm just 602 01:23:45,660 --> 01:24:00,150 Abhay Ashtekar: Trying to understand the direction I'm thinking, or is it more considered to be more promising that even though you're using this canonical language YOU REALLY WANT TO GO ALONG PARTS integral, for example, or on the lines of something. I mean, maybe not lying, but 603 01:24:00,270 --> 01:24:02,190 Abhay Ashtekar: Something like what she was saying, and so on. 604 01:24:02,430 --> 01:24:07,530 Abhay Ashtekar: So I'd like to understand your views about dynamics in general. I mean, anybody not just you, but around anyway. 605 01:24:08,430 --> 01:24:09,510 Daniele Pranzetti: Yeah, so 606 01:24:11,250 --> 01:24:22,020 Daniele Pranzetti: One could i mean the the motivation for this world was truthful. If you want the sense that they were both trying to understand how to reconcile certain forms with the canonical approach and the sense of maybe 607 01:24:22,410 --> 01:24:38,070 Daniele Pranzetti: Trying to construct them for modern eventually from the canonical point of view, and at the same time to to define probably economical dynamics. So one way to one path that we have is to consider now now boundaries. 608 01:24:39,810 --> 01:24:57,240 Daniele Pranzetti: Because in the case if you will contain outbound this then you can you have a notion of time if you want to you can risk press dynamics as a true time evolution and what we will need to understand then is how the boundary dynamics of this edge modes encodes the buck dynamics. 609 01:24:58,410 --> 01:25:08,040 Daniele Pranzetti: But the idea would be basically to yes to use the boundary dynamic of this degree so further on, and not surface to go to define the dynamics. 610 01:25:09,540 --> 01:25:11,130 Laurent Freidel: You can either. Yes. 611 01:25:12,720 --> 01:25:19,560 Laurent Freidel: Thank you. I like very much that question. I think that's such a hard question for me, I would you know what i see what we're 612 01:25:19,980 --> 01:25:29,820 Laurent Freidel: Proposing right now is, like, in some sense, we're proposing a new playing field and I would, I don't know, I think, because it's a new playing field, we should we should keep an open mind. 613 01:25:30,600 --> 01:25:42,420 Laurent Freidel: And look at both ways of doing it. That is, you know, we should know. You should be able to do it can equally and n by informing kind of evaluate which one is the more efficient and ultimately 614 01:25:43,320 --> 01:25:51,150 Laurent Freidel: Do it in such a way that there's no differences between the two approach that would be a bigger consistency check, but depending on your knowledge and your 615 01:25:51,810 --> 01:25:59,490 Laurent Freidel: You know, I think, I think, or do you know it's a new playing field, especially because now the quantum frame fee, the frame Philippines or quantum operating 616 01:26:01,680 --> 01:26:02,760 Laurent Freidel: So that does 617 01:26:04,260 --> 01:26:11,610 Laurent Freidel: It's not nothing. It's easy or done but but i think you know it's it's like a reciting of 618 01:26:13,440 --> 01:26:25,410 Laurent Freidel: You know, a que je if you want instead of looking on the issue two variables which are not enough to because for the operators. Now we ever he said to see times they sell to our absorbent which may be enough. We 619 01:26:30,540 --> 01:26:40,020 Abhay Ashtekar: Thank you that that's good. So I understand it is a beautiful playing field. So I think it's worth definitely looking at it in great detail. 620 01:26:41,430 --> 01:26:46,290 Abhay Ashtekar: But since you also mentioned that nearly about now surfaces that he seems to be 621 01:26:46,680 --> 01:26:57,900 Abhay Ashtekar: There should be some close relation with what Oregon has been doing either you are or gang or anybody else can comment on that. I mean, in that case also you know he and I were very excited about the fact that 622 01:26:58,530 --> 01:27:06,060 Abhay Ashtekar: All can also had some particle like interpretation, right, and some some particles in fictitious mccaskey space. 623 01:27:06,540 --> 01:27:22,080 Abhay Ashtekar: And so we thought that that is going to be a very, very important way perhaps us have no understanding dynamics, but I haven't seen too much development along that lines and so on. So I would like anybody to comment on all these points. 624 01:27:24,060 --> 01:27:25,590 Daniele Pranzetti: Yeah. So yeah. 625 01:27:25,980 --> 01:27:42,570 Daniele Pranzetti: Just wanted it. In fact, I mean, there are several connection with the work of what can and if you want it. This the frame shield in our formalism plays the role of this point or in the approach of welcome and the sense of freedom prize a complex structure and 626 01:27:45,090 --> 01:27:46,230 Daniele Pranzetti: Fundamental degrees of freedom. 627 01:27:49,230 --> 01:27:58,440 Daniele Pranzetti: It's, it would be the we, it would be important to understand how to recast back dynamics and terms of 628 01:28:00,570 --> 01:28:09,570 Daniele Pranzetti: Bandwidth degrees of freedom. Yeah, the food in the food, the case. And that's, I think, what what it's been a mistake. Getting already 629 01:28:10,560 --> 01:28:27,990 Daniele Pranzetti: Quite a bit. And then, yeah, maybe this new insights that we have now environments which are more somehow familiar to them to G framework could help to clarify how to study boundary dynamics in terms of this particle like parameter ization of 630 01:28:29,040 --> 01:28:30,930 Daniele Pranzetti: Degrees of freedom, but 631 01:28:33,930 --> 01:28:38,550 Daniele Pranzetti: I don't think we haven't really looked too much into that at the moment. Okay. 632 01:28:38,820 --> 01:28:40,950 Abhay Ashtekar: But you're you're struggling in terms of 633 01:28:42,000 --> 01:28:49,560 Abhay Ashtekar: I sold to our and as you do all that I think is all already there in the spin up a prayer framework of. Am I right about that. 634 01:28:51,300 --> 01:28:53,250 Laurent Freidel: Future about decent well though but 635 01:28:53,670 --> 01:28:54,210 Yeah. 636 01:28:55,620 --> 01:28:56,010 Laurent Freidel: Anyway, 637 01:28:56,130 --> 01:28:58,050 Abhay Ashtekar: Yeah, because I sell to our because of this. 638 01:28:59,070 --> 01:29:01,830 Abhay Ashtekar: Freedom, having to do with it. So maybe we should answer. 639 01:29:04,830 --> 01:29:06,690 Marc Geiller: And we lost him. Unfortunately, he's 640 01:29:07,260 --> 01:29:10,890 Abhay Ashtekar: Okay, so I mean so to our was because there was this 641 01:29:11,910 --> 01:29:14,550 Abhay Ashtekar: Freedom in rescaling the spinners. 642 01:29:15,930 --> 01:29:27,060 Abhay Ashtekar: There was a it was not completely against you know it is not fixed. You could reschedule each of the spinners keeping to the normalization condition and so on, but okay. 643 01:29:27,630 --> 01:29:30,570 Laurent Freidel: Maybe, maybe that's the boost component of the software which is 644 01:29:30,600 --> 01:29:32,790 Abhay Ashtekar: Yeah, that is exactly the most important visitor. 645 01:29:32,850 --> 01:29:34,590 Laurent Freidel: You know that I would that I would agree. 646 01:29:36,420 --> 01:29:43,530 Laurent Freidel: I mean, you're in some sense, because you are poor cat Andrew, but we focused on the massive representations, because it's very hard work. 647 01:29:44,040 --> 01:29:55,140 Laurent Freidel: But, but, of course, you can think about the mass last presentation. So, and, and, and as we know there's two masters limits right of like a presentation. One is the usual mastery summit. 648 01:29:55,710 --> 01:30:12,000 Laurent Freidel: Which would correspond to go into another surface and the other one is like the continue speed limit which you which corresponds going to beta gamma equal zero. So there is again, there's a lot to be done in that direction. But, but now that we have a coven formulations of all cases. 649 01:30:13,410 --> 01:30:14,430 Laurent Freidel: You know, it's clear that 650 01:30:15,450 --> 01:30:21,150 Laurent Freidel: They shouldn't be a disconnection between the chemical energy isn't space likes her face faces. 651 01:30:22,470 --> 01:30:22,980 Laurent Freidel: But it's not 652 01:30:24,000 --> 01:30:26,520 Abhay Ashtekar: Yeah, I agree. It's very, very beautiful. Thank you. 653 01:30:32,280 --> 01:30:34,440 lsmolin: You are going to introduce matter. 654 01:30:35,670 --> 01:30:50,670 lsmolin: Matter show up in these boundary observable where if supposing you had some now radiation Maxwell field crossing the boundary which, where would you see that in the extension of these equation. 655 01:30:51,360 --> 01:31:01,260 Daniele Pranzetti: So there would be recent sources for the momentum. I was referring to, because that is really them. It's really like that is the real punk or a 656 01:31:02,280 --> 01:31:18,930 Daniele Pranzetti: Algebra, the momentum society from our system. So for instance, if you have a particle, you can now talk about particle momentum and the source these charges with Nike doing three dimension basically good 657 01:31:20,850 --> 01:31:21,090 Laurent Freidel: Maybe 658 01:31:21,690 --> 01:31:29,610 Laurent Freidel: Yeah clarification. Is that your ear. The newly talked about an elemental quick 100 which is the only associated geometry. 659 01:31:30,120 --> 01:31:39,540 Laurent Freidel: And this one should not be confused with this particular like momentum. Right. Forget algebra and the relationship between the two is beautiful is that the elemental 660 01:31:40,110 --> 01:31:48,630 Laurent Freidel: Momentum is associated with the frame shielded say but the particle momentum. If you look at the formula is energy to the differential of the frame. 661 01:31:49,200 --> 01:32:04,680 Laurent Freidel: So, so in some sense what we're hoping for is that the physical moment the physical political momentum becomes from a deeper structure, you know, by, by taking differences. It's a moment of element and momentum between two ages. 662 01:32:06,540 --> 01:32:12,780 lsmolin: Yes, it's supposed to correspond to something like a distortion or disturbance in the 663 01:32:13,770 --> 01:32:17,010 Laurent Freidel: Change in your element or momentum. So 664 01:32:18,870 --> 01:32:20,880 lsmolin: The defect, a defect as well. 665 01:32:21,780 --> 01:32:24,840 Laurent Freidel: Yeah, yeah, the defect in the conservation. Yes. 666 01:32:24,930 --> 01:32:25,320 Yes. 667 01:32:28,800 --> 01:32:29,220 simone: Hello. 668 01:32:30,300 --> 01:32:37,110 simone: Yes. Well, first of all I wanted to say that the fact that you have continue operator. The corresponds to 669 01:32:37,680 --> 01:32:52,140 simone: The twist tangled sigh of the twisted geometries. I think it's really cool. And I'm looking forward to seeing the details in the papers you said are coming out soon. And then I had a curiosity about these elemental porn curry point of view, you're pushing 670 01:32:53,190 --> 01:32:58,260 simone: For instance, and in their conclusions. The third point was, this is embedding in 671 01:32:59,640 --> 01:33:07,410 simone: In the punk era group and then I remember one of the things that I looked at was a similar perspective, but we did embedding in 672 01:33:08,040 --> 01:33:17,640 simone: The conformal group so forth to which is very natural may look like a just academic question, but it's very natural, from the point of view of the two story a parameter ization 673 01:33:18,120 --> 01:33:22,560 simone: Of the start of a cell to see. And there are two, you can see that the simplicity constraints. 674 01:33:23,190 --> 01:33:29,670 simone: Break. They can form a group down to Lauren to with one of the simplicity constraint being interpreted as the delegation operator. 675 01:33:30,420 --> 01:33:38,070 simone: And I was wondering what one interest in Google form a group is that is semi simple and like they conquer a group. And I was wondering if these is 676 01:33:38,670 --> 01:33:50,100 simone: A further enlargement that may be of some hypothetical using these bigger playground or whether you have reason to suspect that these elemental conquer is the end of the story. And there's no need to go larger 677 01:33:53,100 --> 01:33:53,730 Daniele Pranzetti: I'm 678 01:33:54,810 --> 01:33:59,610 Daniele Pranzetti: Free in order for lawrenson violence to be restored. This is enough now. 679 01:34:01,890 --> 01:34:15,540 Daniele Pranzetti: We will know if this will be at me. We will probably. These are not all the edge modes that are necessary in the sense that we know for instance that we need Edge mode for for the different constraint to be included and 680 01:34:17,400 --> 01:34:21,690 Daniele Pranzetti: If there is an interpretation on those lines of, I don't know, but it's 681 01:34:22,800 --> 01:34:31,560 Daniele Pranzetti: Maybe once you try to really work out. They twisted john eviction more and they're trying to reconstruct their autonomy from this 682 01:34:32,820 --> 01:34:44,430 Daniele Pranzetti: Body bolts, maybe it would be more clear if what you're suggesting, actually. Yeah, it can be implemented at the moment, maybe Lauren as their idea or no. 683 01:34:44,520 --> 01:34:51,210 Laurent Freidel: Yeah, yeah. No, I agree with you. It's not. It is not the maximum maximally extended algebra. That's clear. 684 01:34:51,780 --> 01:34:59,520 Laurent Freidel: Because we don't have to. We need an extension to get the como charge for instance that he hasn't talked about. But that's a very interesting suggestion Simoni so 685 01:35:00,330 --> 01:35:09,840 Laurent Freidel: Yeah, we should look into, you know, whether that maximally extended algebra is the one that leads to Twister. For me, I mean that's an interesting conjecture. 686 01:35:11,520 --> 01:35:13,710 Laurent Freidel: That would be amazing. 687 01:35:14,760 --> 01:35:23,400 simone: If you want to get the coma algebra. Another comment is that you might want to look at these exact three for my the alpha does the job for you. 688 01:35:24,030 --> 01:35:26,250 Laurent Freidel: Rarely, we have he has a slide about that. 689 01:35:26,940 --> 01:35:29,190 simone: We have ongoing discussion about 690 01:35:30,840 --> 01:35:32,310 Laurent Freidel: The need to control the next slide. 691 01:35:32,850 --> 01:35:35,100 Daniele Pranzetti: Yeah, so just to 692 01:35:35,160 --> 01:35:35,820 Secret 693 01:35:36,990 --> 01:35:38,100 Daniele Pranzetti: Nights. 694 01:35:40,140 --> 01:35:42,000 A week okay 695 01:35:44,940 --> 01:35:45,150 Yeah. 696 01:35:47,880 --> 01:35:48,630 Daniele Pranzetti: So yeah, you can 697 01:35:49,770 --> 01:36:03,240 Daniele Pranzetti: You see basically the the coma charge can be attained by adding an extra term of this form here is this TED is so if you introduce the space time normal in your face base. 698 01:36:03,780 --> 01:36:13,110 Daniele Pranzetti: Then you can you can show that basically if you add this to the one that we already have the boundary potential that we use so far that you can get the comet charge 699 01:36:13,740 --> 01:36:30,150 Daniele Pranzetti: Which is an animal to there is a some exactly the same. Another way to write the potential that you wrote The, the, I think in Taiwan that we use plus this extra piece here that would give the boundary potential in fact is this original here that I worked on you. 700 01:36:31,500 --> 01:36:40,980 Daniele Pranzetti: So introducing these extra edge months here, then these two notes spaces and normally that that would be the next step to 701 01:36:42,060 --> 01:36:42,600 Daniele Pranzetti: Recovery. 702 01:36:43,620 --> 01:36:44,520 Daniele Pranzetti: The common challenge. 703 01:36:45,030 --> 01:36:55,110 simone: So you're listening to respect is that I should really think of these additional alpha, the way used to call it or if you want to call it, it is there as an Edge Mode effect. 704 01:36:56,910 --> 01:36:58,710 Daniele Pranzetti: Yeah, I mean, it's 705 01:36:59,760 --> 01:37:02,130 Daniele Pranzetti: That's the perspective that we're trying to 706 01:37:02,400 --> 01:37:02,580 Get 707 01:37:04,110 --> 01:37:16,680 Daniele Pranzetti: That, in fact, you can see that that charger. You try to recover recover your potential generates this as an extra piece of the boundary symmetry which is not really the same one that 708 01:37:18,060 --> 01:37:32,520 Daniele Pranzetti: Is not a tangential metric is more like the normal metrics. So it's the metric in the normal plane to the surface, which in a sense, it's kind of dual to their search for that we have. It's, I suspect that there is a traditional and once we implementing PC constraint, but 709 01:37:36,060 --> 01:37:39,330 Daniele Pranzetti: It's, it's, it's a very different piece of the algebra that you reveal 710 01:37:40,020 --> 01:37:41,310 simone: So we pause it at the term. 711 01:37:41,310 --> 01:37:46,890 simone: By hand but you're actually revealing a deeper understanding behind it. Basically, yeah. 712 01:37:46,950 --> 01:38:02,490 Daniele Pranzetti: Yeah, it's, it's in any can be inverted it your way in this way as a sum of all these different terms then you convert it, you have a clear face be structure, you know, which competes with what you can compute brackets. 713 01:38:04,350 --> 01:38:18,270 Abhay Ashtekar: But you did not because certainly here a little bit, because you're getting Hamiltonian to be the coma charged with a specific numerical factor, but the numerical factors are quite different for momentum and angular momentum for the energy and angular momentum. 714 01:38:18,600 --> 01:38:21,060 simone: Presumably is calmer, just for the tangential 715 01:38:21,330 --> 01:38:21,780 simone: Yeah yeah 716 01:38:22,710 --> 01:38:26,010 simone: To get the additional I excited term. 717 01:38:26,280 --> 01:38:26,940 Daniele Pranzetti: Yeah yeah yeah 718 01:38:27,630 --> 01:38:31,140 Abhay Ashtekar: So, so these are just engine, that is to say just rotations. 719 01:38:31,350 --> 01:38:33,240 Daniele Pranzetti: Yes, yes, yes, yes, yes. Okay. 720 01:38:33,480 --> 01:38:34,140 Abhay Ashtekar: Okay, good. 721 01:38:39,690 --> 01:38:40,530 Jorge Pullin: Other questions. 722 01:38:43,680 --> 01:38:45,120 alejandroperez: Yeah, I have a question. 723 01:38:47,220 --> 01:38:52,590 alejandroperez: At the end, you showed this quantum numbers associated to to your 724 01:38:54,210 --> 01:39:03,810 alejandroperez: semen tree generators. And so, so which evokes you know quantum states in a healer space so are 725 01:39:05,550 --> 01:39:13,830 alejandroperez: So you were calling everything continue until the very end. So, but I suppose when you talk about this quantum numbers you're thinking of 726 01:39:14,700 --> 01:39:29,850 alejandroperez: The X on your boundary punctures as you as you mentioned at the beginning. Is that right, and if it's so mean. Do you, do you know already how to construct the hero space without of, I mean, 727 01:39:30,360 --> 01:39:38,190 alejandroperez: You talked about these quantum states, but do you know what the hero spaces where do they live. I mean, the analog of the, you know, speed networking 728 01:39:39,000 --> 01:39:41,130 Or do something to be 729 01:39:42,450 --> 01:39:53,040 Daniele Pranzetti: What. So yeah, it's true. I mean, this would be the if you want this state side would be like edge lingo hyperspace in the quantum theory. 730 01:39:53,490 --> 01:40:08,820 Daniele Pranzetti: Now the possibility to construct the hyperspace would be to use the twisted john three approach in a sense of reconstructing the autonomy of the door graph from the data of the twisted geometry. 731 01:40:09,840 --> 01:40:19,530 Daniele Pranzetti: reconstructing the connection from this list angle the normals, the frames year associate today two faces. 732 01:40:20,760 --> 01:40:30,300 Daniele Pranzetti: We haven't really looked into that yet. So this is the, the idea that one possible way to, we call it the healer space that you're 733 01:40:31,350 --> 01:40:31,980 Daniele Pranzetti: The you're asking 734 01:40:34,650 --> 01:40:51,180 Daniele Pranzetti: Because I mean there's no direct etc. See connection to associate with this, such as the algebra, if you if you just start from the content theory. So one possibility is to yet we use the trees, the geography philosophy to construct that 735 01:40:53,250 --> 01:40:54,540 May be fighting effectiveness. 736 01:40:55,710 --> 01:41:07,770 Laurent Freidel: At something about that. So yeah, this one on numbers are about. Now, do you think you have to appreciate is that all these are surprising to continue our local so that is there is proportionality of delta x, y. 737 01:41:08,670 --> 01:41:17,700 Laurent Freidel: And you follow called algebra as a very singular to quantify in the continuum. Now the important thing here is that the full algebra contains a diff s 738 01:41:18,750 --> 01:41:27,270 Laurent Freidel: Okay, which which showcase that the prime and create some charges. So anyway, so I think you know it's not done but but 739 01:41:29,010 --> 01:41:33,120 Laurent Freidel: It is possible to go. I think beyond a loop cavity. 740 01:41:34,260 --> 01:41:44,430 Laurent Freidel: Quantization if you include into the mix your presentation of the different offers but that's that's that's something that will come in the future. 741 01:41:45,360 --> 01:41:50,790 Laurent Freidel: That anybody can think of. But that's a very important piece of the of the information. If you think about look at 742 01:41:51,450 --> 01:42:03,870 Laurent Freidel: The different Sufism group is just treated cinematically whereas now we do have a generator a canonical generator that moves to point around and and and that changes a lot, the way we think about quantization. 743 01:42:05,940 --> 01:42:13,590 Abhay Ashtekar: Thank you. So then also to Alex, this question is that decides at the moment of formal thing. You don't know what it is, is that correct 744 01:42:14,130 --> 01:42:28,290 Laurent Freidel: They are doing the same size as the size of. Look at the size you would suppose you take your sphere and you discreet is Ethan You just say that only a finite number of cells are activated, then these other loop gravity. Right. 745 01:42:29,070 --> 01:42:38,130 Abhay Ashtekar: No, but I mean I just said, we are in the continuum. So we should discuss anything with. So we just have some graphs and then the size of those those networks of 746 01:42:38,760 --> 01:42:46,290 Abhay Ashtekar: And then I thought the answer to the next question was going to be that you've got this big networks that is the workspace and then you got this punches. 747 01:42:46,680 --> 01:42:50,730 Abhay Ashtekar: Which is the sections of the spin networks to the boundary 748 01:42:51,990 --> 01:42:56,580 Abhay Ashtekar: But the question is about interpreting the cell to see or something that a lot are saying 749 01:42:57,210 --> 01:43:02,940 Laurent Freidel: Her ya know what you're saying is right. So one route is just to do the interview, je type of conversation where you 750 01:43:03,000 --> 01:43:03,300 Abhay Ashtekar: Okay. 751 01:43:03,780 --> 01:43:08,760 Laurent Freidel: Right. So that's one route and that's in that sense that up. Sighs What Sighs What sighs 752 01:43:09,690 --> 01:43:10,140 Laurent Freidel: Space. 753 01:43:10,440 --> 01:43:16,560 Laurent Freidel: That you would assigned to the edges of the spinner took, although the another spin the scenes of the spear more spins. Okay. 754 01:43:17,670 --> 01:43:28,050 Laurent Freidel: So, and then everything we do in Spain low gravity, you can do there with the extended okay what I was saying is that there is something deeper lying beneath is that 755 01:43:29,130 --> 01:43:30,330 Laurent Freidel: The loop gravity. 756 01:43:31,740 --> 01:43:47,490 Laurent Freidel: Does not yet completely allowed to have a full representations of the form of isms acting on the boundary of the sphere, right, and taking that into account can provide regularization ski. I know what I'm saying sounds very theoretical, but believe me, this is this is a 757 01:43:47,910 --> 01:44:00,930 Daniele Pranzetti: Me if you want a proxy for these intermediate step are this tubular structure that I was showing you before, where you can have a part of this defense to represented in terms of this, the formation of the circles. 758 01:44:01,830 --> 01:44:11,880 Daniele Pranzetti: Around the puncture so it's not the full defense by it's you know it's a proxy for for defense which captures some parts of the of the symmetry algebra. 759 01:44:13,170 --> 01:44:20,760 Daniele Pranzetti: Which is a generalization of if you understand speed networks where you extend their this the links to cubes. 760 01:44:22,680 --> 01:44:31,680 Daniele Pranzetti: You can understand this new control numbers in terms of the formation of the circles around the punctures so that's a proxy towards what we're on 761 01:44:33,240 --> 01:44:33,990 Daniele Pranzetti: Suggested 762 01:44:34,620 --> 01:44:40,740 Laurent Freidel: In fact, it goes back to a very old problem that you know very well I buy a new gravity there is when you we know 763 01:44:41,220 --> 01:44:42,480 Marc Geiller: We lost by I think he 764 01:44:44,040 --> 01:44:45,450 Marc Geiller: It will. Yeah. 765 01:44:45,510 --> 01:44:55,320 Laurent Freidel: Anyway, Christmas will not hold on, which is that when you go to the boundary, you know, a puncture space or presentation of gravity election simultaneous equations or what is the 766 01:44:55,800 --> 01:45:05,790 Laurent Freidel: What is the statistics. So what is the action. How does the D from officer groupies represent represented by the exchange of on the exchange of these functions. 767 01:45:06,660 --> 01:45:09,720 lsmolin: Now. But actually that's given by the level. Okay. 768 01:45:10,020 --> 01:45:19,890 Laurent Freidel: No, we don't know. There's several iPod is like some papers, take them as distinguishable some papers takes they might indistinguishable the diversion of 769 01:45:20,340 --> 01:45:28,710 Laurent Freidel: Which is the most accepted is that there are distinguishable either of these things spin and indistinguishable. They are the same speed. And there's a collections of different statistics. 770 01:45:28,980 --> 01:45:30,120 lsmolin: I agree. 771 01:45:30,210 --> 01:45:46,800 Laurent Freidel: But it means. It means that what we know is we know that if you permit the point. The point opinionated. But what phases appear is not known. It's pretty specific. And now these phases we have the possibility to derive them, not just randomly selected. 772 01:45:47,940 --> 01:45:56,940 Laurent Freidel: And accounting depends crucially under absolutely crucial and you can get any number for the entropy, depending on what statistics you give these punctures 773 01:45:58,320 --> 01:46:09,630 lsmolin: But this is another discussion, it's outside of Daniel is talk, but let's have it some time either because I've always suspected that there's only one right answer to this, and it's the one given by the onion. 774 01:46:12,540 --> 01:46:13,080 lsmolin: And sharing, but 775 01:46:13,590 --> 01:46:15,990 Laurent Freidel: Maybe that's not the one that is used to 776 01:46:16,140 --> 01:46:20,160 Laurent Freidel: Shares most popular what most people use just 777 01:46:20,790 --> 01:46:22,770 lsmolin: Just here classical stuff. 778 01:46:23,460 --> 01:46:31,830 Laurent Freidel: Where they use a mix like friends do anyway. The, the most popular one is a mix, where there are sometimes distinguishable sometimes in distribution. 779 01:46:32,880 --> 01:46:33,480 lsmolin: Yes. 780 01:46:37,050 --> 01:46:39,570 lsmolin: The direction the evolution of the discussion. 781 01:46:39,600 --> 01:46:44,910 Laurent Freidel: But if it is an open question. What is the spin of these functions know those statistics. 782 01:46:52,980 --> 01:46:53,820 Jorge Pullin: Any other questions. 783 01:46:59,610 --> 01:46:59,940 Jorge Pullin: Again,