0
00:00:00,000 --> 00:00:00,510
On that
1
00:00:02,399 --> 00:00:05,430
Eugenio Bianchi: For the invitation. Yeah, so
2
00:00:06,750 --> 00:00:17,340
Eugenio Bianchi: The panel includes me Simone and Jonathan and we have the scarcity of the last weeks to try to organize something we always going to be a useful for the
3
00:00:18,750 --> 00:00:24,630
Eugenio Bianchi: International community same united community. I'm going to start with a part that is
4
00:00:27,480 --> 00:00:37,020
Eugenio Bianchi: That is about the symbol lipsticks and going to introduce the definitions and some of the properties and hopefully we can organize the discussion in such a way that
5
00:00:37,530 --> 00:00:52,800
Eugenio Bianchi: Most of the questions can be phrased in the four more questions about single vertex questions about few vertices and questions about many vertices. And I'm going to cover these five points CI and then I leave me with to see mana.
6
00:00:54,060 --> 00:01:03,780
Eugenio Bianchi: So definition of the vertex now will be brief. Take at most 10 minutes to cover this so definition of the vertex
7
00:01:06,420 --> 00:01:25,320
Eugenio Bianchi: Some preliminaries Lauren's group and representations and the definition of the Y map. The thing that the PS in as a principal ingredient into the Lawrence grow into the stream from the Renaissance painful. So if you follow these points.
8
00:01:26,430 --> 00:01:35,100
Eugenio Bianchi: I have festival la Uber space that carries a unitary reducible representation or the Lawrence group is labeled by
9
00:01:37,110 --> 00:01:48,210
Eugenio Bianchi: real number p and an integer k and in the second line and you can see unitary video super representation service YouTube as we are familiar with labeled by Jay
10
00:01:49,440 --> 00:01:53,190
Eugenio Bianchi: Now if I introduce a time like vector
11
00:01:54,270 --> 00:01:54,690
Eugenio Bianchi: Team.
12
00:01:55,710 --> 00:02:05,850
Eugenio Bianchi: And look at the subgroup of the Lawrence group that preserves this time like letter this defined. So one specific little group one specific issue to we've been other Lawrence group.
13
00:02:06,450 --> 00:02:15,330
Eugenio Bianchi: And in particular, now I can speak about generator. So Lawrence transformations in terms of rotations that preserves these facilities factor in booths.
14
00:02:17,070 --> 00:02:30,090
Eugenio Bianchi: Now in the space that carries these unitary representation of the Lawrence group, but I can introduce a basis and our normal basis that simultaneously Dahlia analyzes
15
00:02:30,660 --> 00:02:47,460
Eugenio Bianchi: The two Kazimierz or the Lawrence group and then the Casimir at square one of the rotation group and alien one specific direction is it ok so we've got these
16
00:02:50,040 --> 00:02:56,250
Eugenio Bianchi: Objects. Now I can define a map the wind map that sense of vector imagery
17
00:02:57,420 --> 00:02:58,170
Eugenio Bianchi: In the
18
00:03:00,630 --> 00:03:01,230
Eugenio Bianchi: Percentage
19
00:03:02,400 --> 00:03:23,970
Eugenio Bianchi: rotation group into a vector in the representation of PK of the Lawrence group. It's a specific representation, k is equal to j MP depends on a continuous parameter gamma, which is gonna turn out to be the music Burberry misty parameter times three plus one and
20
00:03:26,250 --> 00:03:39,390
Eugenio Bianchi: When, when these metals were first introduced for defining the Lawrence and spin for model the reference for us was this very complete buco rule. And now there's a primary that they
21
00:03:40,560 --> 00:03:45,000
Eugenio Bianchi: Introduce really all the elements that are necessary. It is the primary by appear mafioso
22
00:03:46,770 --> 00:03:55,860
Eugenio Bianchi: For in case one is not familiar with these unitary reducible representation. So the Lawrence rupa because 40 cents in quantum field theory.
23
00:03:56,790 --> 00:04:04,080
Eugenio Bianchi: We learn the final dimensional representation which are not unitary, and then some infinite dimensional representation says, I don't feel space.
24
00:04:04,410 --> 00:04:15,420
Eugenio Bianchi: So the simplest more familiar. Think of the sky. He is if you consider the hydrogen atom, the original trauma as a group that is larger than the rotation group.
25
00:04:16,560 --> 00:04:30,120
Eugenio Bianchi: For bounced states this group is so for Euclidean group that corresponds to the presence of these additional symmetry generated by the lens vector. And so, but if you look at scattering states.
26
00:04:31,200 --> 00:04:33,570
Eugenio Bianchi: These are representations of the Lawrence group.
27
00:04:34,620 --> 00:04:47,070
Eugenio Bianchi: Representations of a specific kind that is very similar to the one. Consider the there's a continuous parameter analogous to gamma that tells us the impact parameter, it is continuous. Okay.
28
00:04:48,270 --> 00:04:53,040
Eugenio Bianchi: So this is the mathematics behind the end I introduced already why this
29
00:04:54,510 --> 00:05:06,330
Eugenio Bianchi: Is a central object. Now, the definition of the vertex in I'm referring to the angle Perera Rovelli living vertex. The Laurentian one
30
00:05:07,980 --> 00:05:10,260
Eugenio Bianchi: Restricting to the case of
31
00:05:11,490 --> 00:05:18,450
Eugenio Bianchi: Simply shall geometries is the one for all new pattern gravity introduced by Kaminski cielo Scandinavian dusky
32
00:05:19,500 --> 00:05:23,190
Eugenio Bianchi: The ingredients at the following Tuesday graph gamma
33
00:05:24,390 --> 00:05:26,310
Eugenio Bianchi: We are going to think of this graph as the
34
00:05:26,370 --> 00:05:28,260
Eugenio Bianchi: Bounce that graph.
35
00:05:28,560 --> 00:05:31,320
Eugenio Bianchi: Of a selling space time. So a finite
36
00:05:33,060 --> 00:05:36,480
Eugenio Bianchi: Graph without boundary at this point is so we need and then
37
00:05:37,560 --> 00:05:41,940
Eugenio Bianchi: As usual, to the links and the notes of the graph associates means in English whiners
38
00:05:43,440 --> 00:05:52,140
Eugenio Bianchi: You use this map to inject states GM minus two states in the representation of the Lawrence group.
39
00:05:53,340 --> 00:06:05,970
Eugenio Bianchi: And once you do that, the vertex amplitude is defined as in this formula. So as you see, it's similar to the expression of our speed network evaluation. There are intertwined some notes connected we
40
00:06:06,600 --> 00:06:21,810
Eugenio Bianchi: Own links and object that contains the wind map contains the barbarian UFC parameter and there are integrations over the Lawrence group that make it running Lawrence invariant and
41
00:06:23,070 --> 00:06:26,070
Eugenio Bianchi: One of the integral car is dropped because
42
00:06:27,630 --> 00:06:35,070
Eugenio Bianchi: Via that group money for the Lawrence group is non compact and that is one region and seeing these
43
00:06:37,290 --> 00:06:46,770
Eugenio Bianchi: Integrations Instagram and therefore we can fix one to one, otherwise we will get up three of divergence. So this defines completely a quantity
44
00:06:48,330 --> 00:06:58,410
Eugenio Bianchi: That can be computed in fact can be computed medically and soon I will discuss many of the techniques and many of the reasons why it's important to complete it numerically.
45
00:06:59,820 --> 00:07:00,960
Eugenio Bianchi: And can be studied.
46
00:07:03,450 --> 00:07:06,540
Eugenio Bianchi: Analytically, and the values of assumptions have discussed briefly.
47
00:07:08,370 --> 00:07:13,860
Eugenio Bianchi: Okay, point to this was just the definition of the vertex. Now what do we do with that.
48
00:07:15,450 --> 00:07:16,260
Eugenio Bianchi: Well, one
49
00:07:17,550 --> 00:07:19,320
Eugenio Bianchi: remark that is important is
50
00:07:20,610 --> 00:07:26,340
Eugenio Bianchi: He provides a transition amplitude for Rupert and gravity states if you can team call in the following way.
51
00:07:27,750 --> 00:07:33,690
Eugenio Bianchi: Choose a graph gamma in industry network, state your main choose a graph gum out
52
00:07:35,460 --> 00:07:37,380
Eugenio Bianchi: In this associate is inaccurate state.
53
00:07:38,460 --> 00:07:40,650
Eugenio Bianchi: Assume 40 cents, the two graphs.
54
00:07:42,690 --> 00:07:45,750
Eugenio Bianchi: Coincide everywhere except in a compact region.
55
00:07:47,280 --> 00:07:55,800
Eugenio Bianchi: Gamma and the elementary transition period between one state and the other is declared to be a gamma
56
00:07:56,940 --> 00:08:02,100
Eugenio Bianchi: I'm not giving now the revisions. I'm stating what is the vertex now.
57
00:08:02,760 --> 00:08:10,590
Eugenio Bianchi: Especially that I gave us in terms of spins and intertwine hours, but often quantum gravity, we were we were the representations for his son Solano means or
58
00:08:11,490 --> 00:08:21,000
Eugenio Bianchi: Spins and normal so speed Nouriel representation or or or a morphic representation and all of these expressions are being studied and that useful in various situations.
59
00:08:21,330 --> 00:08:30,720
Eugenio Bianchi: So the remark is that the boundary state space for this first X is the loop quantum gravity universe space on a graph, the one declared above
60
00:08:31,860 --> 00:08:38,910
Eugenio Bianchi: The other two remarks are there is this continuous parameter that you can think of it as a coupling constant gamma
61
00:08:39,510 --> 00:08:48,900
Eugenio Bianchi: These, these the Burberry music parameter in know that appears in the theater we we to independent floors in this formulation, at least.
62
00:08:49,740 --> 00:09:02,880
Eugenio Bianchi: It certainly appears in the spectrum of geometric operators. Together we g and h bar always reach bar gamma and you know the place is a PR alone as, for instance, gamma plus one minus one.
63
00:09:03,960 --> 00:09:07,140
Eugenio Bianchi: These are passing the dynamics. These are the
64
00:09:08,430 --> 00:09:24,360
Eugenio Bianchi: parity of terms in the action at the classical level is a PR source. So in India ME, TONY I'm formulation India and the spin from vertex. You see, to. He then into these why map it contains gamma is the only object in the dynamics that contains gamma
65
00:09:27,120 --> 00:09:36,090
Eugenio Bianchi: OK, so moving ahead the point three, how is this related to for the geometry.
66
00:09:38,580 --> 00:09:47,970
Eugenio Bianchi: So I'm giving again the disc patronizing the previous page. We have a spin actor can transition amplitude, but now I interpret notes as quantum police
67
00:09:49,350 --> 00:09:51,270
Eugenio Bianchi: By interpreting them as quantum police
68
00:09:52,350 --> 00:10:10,860
Eugenio Bianchi: I can give a geometric picture and the fourth dimension of geometric picture arises. So for a sensor. The initial state. You can think of it as consisting of n in notes, each one a quantum body either on a given interval weiner. Similarly, for the out state.
69
00:10:12,270 --> 00:10:22,290
Eugenio Bianchi: Now something interesting happens. So when I give the spin that we're safe with decent test whiners the factor I state of various interest whiners. This is a state of police
70
00:10:23,010 --> 00:10:36,630
Eugenio Bianchi: in three dimensional space, the wine map embeds them in our forum fourth dimensional space and the by construction introduces a for vector and Polydor or leave in
71
00:10:38,220 --> 00:10:41,790
Eugenio Bianchi: Three dimensional space are going to this for vector now.
72
00:10:42,810 --> 00:10:44,340
Eugenio Bianchi: imposing the that
73
00:10:48,060 --> 00:10:58,740
Eugenio Bianchi: The specific format of the Y map in the specific form of our gamma enters. As a consequence, the formula here in blue. That tells us that
74
00:10:59,220 --> 00:11:17,460
Eugenio Bianchi: Each piece of the police later on as a three normal that slicing the plane where the police are nice and these partially fixes the map why gamma. If we impose the total matrix elements of these objects that tells us what is the normal face k minus gamma
75
00:11:18,570 --> 00:11:39,090
Eugenio Bianchi: Is zero matrix elements. And we also impose that the dispersion is minimized. Then the map is completely fixed by what I declared in the first slide on the wind up. So this is one period around in 3D space if you want to change the frame you change it with a Lawrence transformation G.
76
00:11:40,320 --> 00:11:59,670
Eugenio Bianchi: Lauren Symbian projection of these set of police geese, a four dimensional object it is Lawrence environment that is again the worst example shoot a note that these special as a Christian cemetery, as was originally discussed in. Yeah, yeah, one of the papers of catalog.
77
00:12:01,440 --> 00:12:05,640
Eugenio Bianchi: In in the late 90s as a requirement for this versus amateurs.
78
00:12:08,490 --> 00:12:13,440
Eugenio Bianchi: Okay, so this gives a geometric picture now point for
79
00:12:15,120 --> 00:12:23,160
Eugenio Bianchi: There is one test that is a detailed test of the geometric properties.
80
00:12:24,270 --> 00:12:39,900
Eugenio Bianchi: That I like to phrase in this form as single verse six correlations. So instead of describing the asking topics of diverse Tex. I'm telling you directly, what are the properties of correlations of the vertex
81
00:12:41,100 --> 00:12:49,500
Eugenio Bianchi: Okay, so take a Laurentian vertex simply to the let's assume for simplex. This is the case, it has been a force work. It worked out in the Laurentian.
82
00:12:49,980 --> 00:13:00,450
Eugenio Bianchi: Choose Aquarian binaries say they speak to a classical geometry. It's the one Laurentian for simplex look at correlations for instance area, area right angle, angle angle.
83
00:13:01,260 --> 00:13:09,360
Eugenio Bianchi: In the synthetic analysis when the boundary. He speaks are now the following quantity you assume that the spin some laughs
84
00:13:10,110 --> 00:13:17,010
Eugenio Bianchi: But the music parameter is sent to zero. We've areas fixed one finds it all of these correlations
85
00:13:17,730 --> 00:13:26,220
Eugenio Bianchi: match exactly simply show correlation. So it could be predicted using registration gravity plus corrections over the gamma
86
00:13:26,820 --> 00:13:37,020
Eugenio Bianchi: So simply show correlation sir recorders and you can associate to these four dimensional object as semi classical interpretation as a four dimensional simplex and
87
00:13:38,280 --> 00:13:46,530
Eugenio Bianchi: I think also it towards in the case of a mediator. Yeah, what is the origin of the matter. Well, this is something that was
88
00:13:47,220 --> 00:13:57,030
Eugenio Bianchi: That I didn't suspect we found it by the tail calculation it disparate you're the last one I could have expected and I
89
00:13:57,540 --> 00:14:14,010
Eugenio Bianchi: Can tell you that the origin is the nominal GDP in the geometry that comes from vector geometry fluctuations. So this is a point to keep in mind when one speaks about the tests and rigidity and robustness of the vertex already at the level of single vertex now.
90
00:14:15,450 --> 00:14:27,750
Eugenio Bianchi: I want to add one last point before closing that is the that is related to the picture of an evil vertex is related to classical theory and degrees of freedom.
91
00:14:28,470 --> 00:14:39,900
Eugenio Bianchi: As you so I never spoke about taking a classical theory and quantum using it, I define the worst example to the show that satisfies a list of properties that are desirable.
92
00:14:41,640 --> 00:14:45,540
Eugenio Bianchi: Now the broke picture, as I understand it, is the following.
93
00:14:46,740 --> 00:14:56,160
Eugenio Bianchi: We know that if you take a topological theory of the BF kind that is a snow local degree of freedom and you can get back. General relativity
94
00:14:56,640 --> 00:15:07,590
Eugenio Bianchi: If you unfreeze degrees of freedom by constraining the field everywhere in the for manifold to be a simple you get back general activity will be infinitely many degrees of freedom.
95
00:15:08,820 --> 00:15:29,460
Eugenio Bianchi: What I in general I call spin forms or spin form action. Is this a similar procedure where the constraint on be is imposed only on two phases of our cellular cellular the composition of the map before this is funny number of degrees of freedom at fixed cellular the composition
96
00:15:30,510 --> 00:15:38,430
Eugenio Bianchi: Therefore, the classic theory should be under control. There are various proposals for our specifically. This is
97
00:15:38,430 --> 00:15:39,120
iPad di Carlo: Don't look.
98
00:15:40,020 --> 00:15:46,440
Eugenio Bianchi: So there are various proposals for spin from actions classic elections, the quantization as it's funny.
99
00:15:47,490 --> 00:15:54,450
Eugenio Bianchi: For a number of degrees of freedom in principle should be immediate. But the constraints that that be it make it non trivial.
100
00:15:56,760 --> 00:15:59,100
Eugenio Bianchi: Party or the second classical strange Mickey material.
101
00:16:00,210 --> 00:16:08,940
Eugenio Bianchi: There is a question on the other line not taking one time seeing enticing researchers ladies classical theory.
102
00:16:09,960 --> 00:16:11,850
Eugenio Bianchi: Which is what has been done, especially in the
103
00:16:11,850 --> 00:16:12,780
iPad di Carlo: Beginning as a
104
00:16:12,810 --> 00:16:20,370
Eugenio Bianchi: Guide for finding diverse. Next, there's a different question of adding one specific proposal for the vertex in wasn't a max.
105
00:16:22,470 --> 00:16:23,460
iPad di Carlo: What is a
106
00:16:23,760 --> 00:16:34,080
Eugenio Bianchi: Condition on the state and on properties of this vertex amplitude. The for raw are being a spin for matching emerge and this question comes with
107
00:16:35,520 --> 00:16:40,650
Eugenio Bianchi: Many sub questions and many tests already at the level of a few birds disease.
108
00:16:42,180 --> 00:16:46,560
Eugenio Bianchi: For which there are specific expectations and also some concerns that
109
00:16:47,820 --> 00:16:52,740
Eugenio Bianchi: Simone and john will discuss and at the level of many verse. This is where
110
00:16:54,120 --> 00:17:06,060
Eugenio Bianchi: Even questions of comfortability and definition become non trivial, so I think I'll stop here and let see Mona continue. And then when there are questions I can add more
111
00:17:12,810 --> 00:17:17,370
simone: Okay, let's see if I'm still able to do that procedure.
112
00:17:23,160 --> 00:17:25,140
simone: Can you see my screen.
113
00:17:26,550 --> 00:17:26,910
Benjamin Bahr: Yes.
114
00:17:28,620 --> 00:17:33,330
simone: Okay, perfect. Thank you, gentlemen, for the introduction. In the first part. So,
115
00:17:34,560 --> 00:17:37,200
simone: In my second part, I would try
116
00:17:42,630 --> 00:17:53,310
simone: And then he began America results within range and vertex the extension of the analytic results missing piece or vertices and some comments on the dynamics. My slides are
117
00:17:54,600 --> 00:18:02,460
simone: A bit maybe dense, but I don't plan to read through all of it. Most of the material is there just for backup. So don't get too worried about it.
118
00:18:03,510 --> 00:18:04,740
simone: Sounds like to
119
00:18:06,450 --> 00:18:15,330
simone: Pick it up from where a general define the model in these more general form that is a priority find on an arbitrary graph.
120
00:18:16,230 --> 00:18:30,720
simone: The actual caveat there is that it is not defined an arbitrary graph completely because the interoperability, there will define us of this integral is not guaranteed for an arbitrary graph in particular, removing one
121
00:18:31,920 --> 00:18:39,240
simone: Node integral is not enough. And in principle is known for a long time. So,
122
00:18:44,700 --> 00:18:49,620
simone: In most of the things about general graphs that I'm interested in will concern grabs their
123
00:18:50,190 --> 00:19:02,370
simone: Dual to the boundaries of politics. And in those cases, removing one result. The integration is fine it but, for instance, if you have things like a tadpole somewhere then these are these amplitude does not exist.
124
00:19:04,740 --> 00:19:14,220
simone: Okay, sounds like the number three. So where do we stand with the valuation. These interior is actually even when it's fine. It is very complicated to evaluate
125
00:19:14,640 --> 00:19:33,660
simone: Because these infinite dimensional madrasas here are highly oscillating and we have many onboarding integrals and we don't have that many analytic results and the metrics are really complicated. So compare these with the 15 J. The one usually deals within BF theory is
126
00:19:35,340 --> 00:19:48,660
simone: An evolution point of view. One way to make progress is to use these representation theory of a cell to see, and in particular the federal data Jordan coefficients can be factors in terms of a pseudo coefficient, which introduces these
127
00:19:49,680 --> 00:19:54,660
simone: Edge dipole looking like amplitude, which the Group of
128
00:19:55,590 --> 00:20:05,370
simone: Students Mr say then rename the booster functions, which I think is very nice because he's the only place where a boost occurs in the range and amplitude. The rest being just an issue to
129
00:20:06,180 --> 00:20:26,520
simone: Amplitude at the vertex. So these factorization here is useful for both analytical no medical investigation and has made it possible to actually compute explicitly this vertex and this is that the values applications. Let me give you some brief overview of some results for instance.
130
00:20:27,630 --> 00:20:45,540
simone: If you're familiar with this dipole cosmology or Francesca Carlos jobim sale for other people. They looked at it, they had some analytic studies, but in principle, using. So these now using this increase your vertex. I'm as I said that was more or really
131
00:20:48,300 --> 00:20:49,500
simone: Analyze vertex, the price.
132
00:20:51,480 --> 00:20:58,020
simone: For voluntary voluntary again for volume vertices are appearing in the same form and not the fallen ones have this increase your case.
133
00:20:58,440 --> 00:21:09,990
simone: So, one can actually compute numerical explicitly designed platoons and get quantitative results. So for instance, one can see that the largest been behavior of the vertex amplitude as a function of
134
00:21:10,590 --> 00:21:20,280
simone: A larger spin on the boundaries. The case faster and faster as the complexity of the form increases. Maybe you could have expected. These but here, there's a quantitative statement.
135
00:21:21,420 --> 00:21:23,580
simone: One can compute correlations for instance.
136
00:21:24,210 --> 00:21:32,730
simone: In dipole cosmology, or people look at this diagram. Initially, it is known that the amplitude factor is is exactly. So there are no correlations between the
137
00:21:33,000 --> 00:21:43,380
simone: Spins here and the spins here correlations only appear when you start something over an internal face and one can you medically compute them. See, for instance, they are positively correlated and the
138
00:22:02,790 --> 00:22:03,030
simone: We
139
00:22:03,780 --> 00:22:05,820
pullin: lost audio after possibly
140
00:22:06,210 --> 00:22:08,760
pullin: positively correlated. I know.
141
00:22:09,180 --> 00:22:11,880
simone: You lost audio. Can you hear me now. Yes.
142
00:22:12,540 --> 00:22:13,050
Okay.
143
00:22:14,160 --> 00:22:19,950
simone: I was saying. Another important application of these metrics concerns the bubble divergences because
144
00:22:20,820 --> 00:22:30,810
simone: From the new man from the sorry analytic estimations these typically provide the lower bounds and there could be surprises there could be things that are underestimated too much.
145
00:22:31,200 --> 00:22:40,170
simone: So Peter use the numerical methods are based on these approach to investigated the seven energy bubble divergence
146
00:22:42,150 --> 00:22:54,810
simone: Turns out that these numerical is very complicated. I don't think is never finished this calculation numerically. But for instance. He looked at the simplified case with a full violent vertex showing that is actually convergent. In the case of the ether and model.
147
00:22:55,500 --> 00:23:04,170
simone: And for these one use the some improve this estimates, which are based on the nomadic supply the just the BF theories to estimate the divergence much higher than
148
00:23:04,620 --> 00:23:12,420
simone: All those the lower bound in the work he did his PhD and there's also been more interesting, very interesting also more recent work by
149
00:23:13,140 --> 00:23:24,150
simone: Good genius and do not the concern evaluations with different genre Jamal then and also four dimensional BF theory more working progress that they would mention later another
150
00:23:25,170 --> 00:23:30,270
simone: Well known well known. Another important application. They probably all of you already known because
151
00:23:30,570 --> 00:23:41,700
simone: You have seen it or heard it presented by me or Peter or Georgia concerned the verification of the identity formula for the single for simplex which was really
152
00:23:42,630 --> 00:23:53,790
simone: Tiring complicated about so very satisfactory, at least as far as Euclidean boundary data are concerned, where one gets a very nice matching
153
00:23:55,860 --> 00:24:03,120
simone: That would improve the matching. You can see there's still some phase discrepancy, or we understand where that comes from.
154
00:24:03,930 --> 00:24:16,470
simone: The matching the similar to the matching one gets for just us for just be BFS you to theory for the orange and boundary data, the situation is not so good. We see we can
155
00:24:17,310 --> 00:24:27,900
simone: Confirm the power of decay and the fact that there is a gamma dependence on the solutions, but this is a simple formula. This is what we have in America Li is is still a long way before these actually bands enough
156
00:24:28,410 --> 00:24:40,230
simone: To get closer to the expected curve, but for that one needs more powerful computer so that one can increase the cutoff in the internet sounds are pushing the speeds to higher values, something which
157
00:24:41,130 --> 00:24:52,320
simone: May be possible. I just heard the from gator in Georgia, that he got access to a very powerful cluster. And so maybe we can employ some of the computing time to extend these
158
00:24:52,830 --> 00:25:01,170
simone: These results here, you'll notice that in these formulas not using the original definition of the model with intertwines but the one with the
159
00:25:02,100 --> 00:25:12,480
simone: With the 3D normal. So, which is the Korean birth example which boys back to this very nice work that we did, we did. There are a very long time ago. We're both still a pretty matter.
160
00:25:13,140 --> 00:25:18,660
simone: And the idea is that if you are reformulate the amplitude as a linear superposition, in terms of
161
00:25:19,080 --> 00:25:28,740
simone: As you do great and states, then you get this nice factorization form which you can use to start this other point analysis. So, this is the expression of the equation vertex amplitude
162
00:25:29,550 --> 00:25:37,680
simone: And the boundary. Did that play an important role. So let me briefly describe them with reached from spins into
163
00:25:41,160 --> 00:25:46,920
simone: The geometric interpretations, the same screen Saturday as intertwines will represent the one
164
00:25:47,220 --> 00:25:57,330
simone: That usual angled incompatible with all the others, whereas these normals allow you to describe all did that. He relinquished seen data. HE DOING AND THAT'S RIGHT. THIS IS A classical feature as opposed to the intertwining one
165
00:25:57,900 --> 00:26:10,800
simone: Now it is natural to classify the boundary data, according to certain subsets, for instance, one can start with arbitrary configurations or one can consider close the configurations to satisfy the crucial constraints on every node.
166
00:26:12,060 --> 00:26:21,090
simone: Among the closed once one can consider those that defined the vector geometries, namely those for which the normal answer pairwise opposite are always anti pattern.
167
00:26:21,960 --> 00:26:30,870
simone: And finally, one can consider data that actually satisfy the angle matching conditions on top of the pairwise opposite condition and these are equivalent to raise your data.
168
00:26:31,740 --> 00:26:39,720
simone: It turns out that choosing these different sub classes of boundary data as be friend that imposes different synthetic behavior on the integral
169
00:26:40,470 --> 00:26:50,220
simone: In particular, in the generic case you want to include in imposes no closure or only closure. There are no solder points and then one is an exponential fall off.
170
00:26:51,090 --> 00:26:59,130
simone: In the case of Ektron geometries. One is one subtle and then there's a powerful falafel with some face. And it's important to stress that these phases arbitrary
171
00:26:59,400 --> 00:27:11,430
simone: In the sense of these gauges dependent. It depends on the orientation of the normals, and not just on the shape of the data heater in the case of Reggie geometries. One is to these things. And then on top of the
172
00:27:26,730 --> 00:27:27,900
Baofei Li: We lost audio again.
173
00:27:34,620 --> 00:27:35,880
Baofei Li: We lost audio again.
174
00:27:44,160 --> 00:27:45,000
simone: Can you hear me.
175
00:27:46,560 --> 00:27:46,950
simone: Oh,
176
00:27:47,040 --> 00:27:48,630
Baofei Li: Yes. Yes, we can hear you now.
177
00:27:49,320 --> 00:27:52,080
simone: I see why should I start again from
178
00:27:55,350 --> 00:27:57,000
simone: What was the last thing you heard
179
00:28:00,180 --> 00:28:03,570
Hal: When you started describing the Reggie case Simoni
180
00:28:20,010 --> 00:28:21,030
We lost audio again.
181
00:28:28,230 --> 00:28:32,490
simone: Let's see what I can try to maybe test my microphone.
182
00:28:33,630 --> 00:28:34,170
pullin: Go ahead.
183
00:28:34,980 --> 00:28:35,460
Yes.
184
00:28:42,030 --> 00:28:42,960
simone: Where was I
185
00:28:44,280 --> 00:28:44,640
Know,
186
00:28:47,760 --> 00:28:56,940
simone: Back. So I wanted to stress that even though the boundary data truly three dimensionally this possible to give them a four dimensional interpretation.
187
00:28:57,300 --> 00:29:03,810
simone: Because if you restrict them to satisfy the Reggie conditions than every three dimensional Reggie geometry or fake data here.
188
00:29:04,530 --> 00:29:11,910
simone: Is the boundary of a flat for simplex. So, one gets a four dimensional interpretation for free is not the case for more general graphs.
189
00:29:12,510 --> 00:29:21,450
simone: So moving to the next slide number seven, very briefly, why is these anti parallel condition useful because
190
00:29:21,750 --> 00:29:27,270
simone: These condition of vector geometry which means that they exist rotation, such that the Normans can be put back to back.
191
00:29:27,600 --> 00:29:34,350
simone: Our brewery doesn't have any intuitive a geometric media, but it turns out that he does have a very simple geometric meaning and he's the following fact
192
00:29:34,890 --> 00:29:41,280
simone: That every occasion for simplex can be projected in our three in a way that it satisfies this condition.
193
00:29:41,970 --> 00:29:52,440
simone: So these are special condition the capture something of the geometry of for simplicity's, however, not every such configuration of airways opposite normals comes from an op them for simplex
194
00:29:52,980 --> 00:29:59,280
simone: They agreed and for simplex only spanner good you mentioned five surface which satisfies the additional angle matching conditions.
195
00:29:59,820 --> 00:30:17,520
simone: This is important to justify give some dramatic picture of why these pairwise opposite condition that plays such an important role in Bartlett's analysis is actually non magical that comes from some geometric description that we know. So on slide number eight. How about the
196
00:30:18,720 --> 00:30:19,650
simone: Show now.
197
00:30:22,590 --> 00:30:32,340
simone: Then jack Jones very important is playing an important role for the interpretation of the geometry of speed forms and also to suggest a way to investigate the semi classical limit.
198
00:30:32,910 --> 00:30:37,890
simone: It's useful to emphasize, and we have you done this with a genuine john that is not an SSRI sufficient condition.
199
00:30:38,250 --> 00:30:47,550
simone: One could find ways of understanding the silica silica leave without invoking a range of behavior in the speed limit. But it's nonetheless a solid, the result also confirmed the from the aromatics.
200
00:30:48,150 --> 00:30:58,740
simone: So, one can then ask the question, what is the synthetic limiter of these generalized vertices which are you all to which are not able to simply says, and this
201
00:31:00,270 --> 00:31:00,900
simone: Was first
202
00:31:03,300 --> 00:31:09,870
simone: And then also device then steinhauser, and more recently by the man of and they showed a couple of novelties
203
00:31:10,500 --> 00:31:22,080
simone: Looking at it. Some explicit example mostly associated with a progressive disease. They showed that there could be two distinct Southern with non Reggie geometries and also show that there could be four or more interesting saddles
204
00:31:22,770 --> 00:31:29,370
simone: So in our group, Mr. Say we took a systematic approach to study the syntax of these generalized vertex
205
00:31:30,060 --> 00:31:38,160
simone: For months, inclusion line graphs and we confirm that these mismatch the geometries and increase the southern multiplicity an individual's genetic features.
206
00:31:38,730 --> 00:31:47,520
simone: The key to achieve this result is actually to go beyond to abandon the beta reconstruction theorem and use a really, these are three dimensional geometry viewpoint that I've been insisting on
207
00:31:48,210 --> 00:31:56,070
simone: And on Slide nine is a quick scan of what happens, what happens is that they can be a little
208
00:31:56,490 --> 00:32:07,560
simone: More than one side or our angle matching it not cheap matching. It's only in the case of triangles that is equivalent to a ship matching. But in general, you might have conforms matches of these type
209
00:32:08,160 --> 00:32:22,290
simone: And these conformity mismatch that Mr Jerome at least admit two distinct samples and it actually looks like the Reggie action in the area times for dimension of the hero angles determined from three dimensional which are well defined. Even if you don't ever energy on it.
210
00:32:23,430 --> 00:32:30,810
simone: So I'm running out of time, so I cannot tell you much more free time being about the details of the structure, unless there are questions. I'll come back to it.
211
00:32:31,740 --> 00:32:43,200
simone: So I would like. So just to answer it. So we know what is the syntax of these more generic vertices. And there are some surprises. They were anticipated by Benjamin and his collaborators.
212
00:32:44,250 --> 00:32:46,230
simone: So now for the dynamics, which is probably the
213
00:32:47,550 --> 00:32:59,040
simone: Most dedicated aspect that you have not is the head is nice green tick marks that we make questions we use, you know, I don't have one, because the question is a little bit trickier. And there's no definite answer unfortunately
214
00:32:59,400 --> 00:33:10,710
simone: So if you use the screen intertwines you will recognize these as diverse example to the full partition function will look like something like this when I'm also something over the speeds in integrating over the normals that defined the Koreans intertwines
215
00:33:11,100 --> 00:33:16,140
simone: This is supposed to be some quantum gravity path in a row. And so the question is whether
216
00:33:16,620 --> 00:33:28,920
simone: The quantum wait at least the question for me is whether the quantum weight is dominated by configurations which are solutions of the have some classical action they correspond to democratize the GR since we are on a discrete I said in here.
217
00:33:30,300 --> 00:33:33,180
simone: Two pieces of information, these financial
218
00:33:34,650 --> 00:33:36,510
simone: Capital F here.
219
00:33:39,390 --> 00:33:52,980
simone: To are necessary for a critical point that behavior in the autonomy to girls are the, the hero ankles. Then second America being the actual entering the speed. So if I just look at what are the configurations that
220
00:33:54,480 --> 00:34:05,790
simone: Vantage the gradient of these action here. I would just get f equals zero immediately. Now I could be tempted to concluded that this means that the some sorry it is wrong. Of course, it should be.
221
00:34:06,420 --> 00:34:21,450
simone: It should have been the the deficit angled should have appeared somewhere. And so instead of just did a hero angle. So if I use these two facts first that the derivative gives me the deficit angle and that
222
00:34:22,590 --> 00:34:26,370
simone: That on shell of the closures angle constraints, it gives me the deputy tango.
223
00:34:26,700 --> 00:34:34,620
simone: And the derivative with respect to the spin. If you vanishes tells me this function is zero and may be tempted to say that the deputy tangles would necessarily be zero.
224
00:34:34,950 --> 00:34:41,430
simone: Which will be bad because then there's no curvature. There's no interesting dynamics in the model, but these argument is wrong.
225
00:34:41,820 --> 00:34:53,460
simone: Because everyone zero is obtainable vanishing respect to the scenes, but f coincides with the deficit angle only if they spent a normal are constrained. And then I cannot do this variation with independent spins.
226
00:34:54,030 --> 00:35:03,930
simone: So I'm more precise analysis is required to see what the dynamics is really like. And to understand these my best intuition is the one that they got from it and go, Reggie calculus.
227
00:35:04,530 --> 00:35:10,530
simone: Because let's not forget that we're getting is not just directly in action in terms of the elements as it is, Reggie calculus.
228
00:35:10,860 --> 00:35:24,780
simone: Or rather, in action in terms of areas and the usual angles, which are defined by this killer products from the 3D normals. And what will surely blank, a long time ago was that these type of structure that arises at the synthetics is consistent with a
229
00:35:29,100 --> 00:35:29,580
simone: new a new
230
00:35:31,890 --> 00:35:32,610
simone: Question is,
231
00:35:36,930 --> 00:35:44,790
simone: Actually a nice and simple calculus. It's equations emotions are a bit of a mess. In particular, if you look at the variation respect to the spin
232
00:35:45,180 --> 00:35:52,860
simone: We get a deputy dangle as I should have written around instead of the, the hero, Michael. Sorry about that. But that's a contribution that comes from these plugins, you multiply your meal.
233
00:35:53,520 --> 00:36:03,990
simone: If I forget about these again of course flatness, but these contribution is there and this becomes equivalent to their education. Only once they've sold all of the equations. He particular also THOSE THE FIX THE LUGGAGE multiplier.
234
00:36:04,620 --> 00:36:12,330
simone: Now the structure of it encourages you to set the structure just described. There's always made me might be optimistic about the fact that the patron model may work.
235
00:36:12,840 --> 00:36:25,500
simone: Because if I interpreted as the exponential of the rejection as bad as as the ride time some delta functions that impose the closure and she matching constraints, then we're looking pretty good.
236
00:36:26,460 --> 00:36:34,470
simone: And if I will get pretty good, then we can move to the really interesting questions which is not just to get the Reggie behavior, but to see about quantum corrections.
237
00:36:35,130 --> 00:36:46,440
simone: However, and I moved to slide 13. This is actually a very fragile structure because if you drop these new term here, you get immediate you lose different solutions and if you
238
00:36:52,500 --> 00:36:59,670
simone: Don't know what is exactly shape or because actually it is not a delta function, but it's some type of GAO Xiang and maybe it's abroad Gershon
239
00:37:00,000 --> 00:37:06,150
simone: They were not looking very good. Then we are losing the prevalence with Reggie calculus and we are losing possibly called the solutions as well.
240
00:37:06,570 --> 00:37:12,690
simone: So that's for me the way of looking at this problem. I never quite succeeded to get these in concrete answer.
241
00:37:13,200 --> 00:37:19,920
simone: On the content most investigations along the years I found that no evidence of this etc and concluded that the model is only for distributions.
242
00:37:20,520 --> 00:37:31,440
simone: And now I personally have technical counter arguments to every of these technical analysis, but don't find it very useful to go into the details here because you would think.
243
00:37:33,450 --> 00:37:39,750
simone: And because they're very technical and it's easy to not agree. Easy. So instead of like to
244
00:37:40,230 --> 00:37:45,960
simone: Consume suggest an alternative which is forget about fighting or a technical details let just let the medical check
245
00:37:46,440 --> 00:37:56,700
simone: And a very simple test ground which has already been discussed in the past is delta three triangulation, which has three four simply says sharing one face. Now this is not the ideal setting.
246
00:37:57,150 --> 00:38:03,660
simone: Because even though there are internal degrees of freedom being some Dominus painful model, the internal face and also the intertwines here.
247
00:38:04,350 --> 00:38:09,180
simone: From the point of view of Reggie calculus. There's no dynamics here because all the edges are boundary edges.
248
00:38:09,510 --> 00:38:28,410
simone: Steel at one can cook up some trivial test, which is to ask that all the boundary data are such that the edge lens are fixed to be either those compatible with curvature or without curvature at these internal internal face and then one can study where whether this been phone and
249
00:38:30,210 --> 00:38:39,210
simone: Internet speed. The one is coming over on the one that is compatible with their edge interpretation or not. These are not to be a non trivial test.
250
00:38:39,720 --> 00:38:44,550
simone: And by not your test. I mean that if you run this test will be f theory, we have to actually fields, it
251
00:38:45,000 --> 00:38:48,780
simone: In the sense that if you choose the boundary data so that the spin should be flat.
252
00:38:49,170 --> 00:38:55,080
simone: Then you get a stationary point for that flat spin. But if you fix the boundary data so that there is curvature, then
253
00:38:55,350 --> 00:39:05,550
simone: There is no stationary face or the spin correspondent for with this curvature solution. And this has been recently beautifully shown by Peter in Georgia with dental medical code and I hope they will
254
00:39:06,870 --> 00:39:15,540
simone: Publish it soon and then move on to the business case, which is what we're interested in the most and hopefully give us a clear answer by the summer.
255
00:39:16,110 --> 00:39:25,830
simone: By the end of the summer, maybe, hopefully. So to summarize, and so if I run or have run over my time. I think that we, these rights and MP to these
256
00:39:26,970 --> 00:39:28,920
simone: Something that we can very well compute with
257
00:39:30,540 --> 00:39:33,570
simone: My main advice is to use the same routine.
258
00:39:35,250 --> 00:39:43,770
simone: And there's lots of work that one can do and at least at some valid point of the work that I would like to see done in the upcoming time
259
00:39:44,340 --> 00:39:51,360
simone: There's hundreds of different signature vertices is also known, of course, there's, there's an issue whether one is really interested in these generalized more than
260
00:39:51,690 --> 00:39:58,200
simone: Or whether one would like to be something tighter somebody that is closer to having only Reggie geometries in the semi classical limit.
261
00:39:58,440 --> 00:40:04,740
simone: And so to modify the model in such a way, and they know the Benjamin, or at least by the bell on the student have been working on this.
262
00:40:05,640 --> 00:40:22,080
simone: As far as the dynamics, the situation is more open for discussions and I've given my advice in my bullet point here and maybe we can come back to it, and I should pass it on to john and sorry again for running too late.
263
00:40:30,360 --> 00:40:32,640
FAU: Okay, alright, just let me
264
00:40:43,200 --> 00:40:47,340
FAU: Do you see the slide is that, am I sharing successfully. Yes. Okay, go.
265
00:40:49,980 --> 00:40:50,640
FAU: Part of the
266
00:40:51,330 --> 00:40:55,380
FAU: Of the panel. I'm going to be talking about these debates on
267
00:40:56,490 --> 00:41:05,100
FAU: Degenerate sectors and the cosine issue and the, the so called flatness problem. Some only talked about this a little bit at the end of his part.
268
00:41:08,040 --> 00:41:10,200
FAU: So, and
269
00:41:11,370 --> 00:41:22,290
FAU: I'm starting with the quantization, which is leading to the PRL model so that one can really starts from the the BF vertex amplitude
270
00:41:23,940 --> 00:41:45,870
FAU: And here I've represented the the boundary state as a coherent state I'm emphasizing that this is a state in the boundary Hilbert space that's peaked on certain values of the discrete be field which is like a discrete polonsky field, these, these by vectors and and the y map as
271
00:41:47,370 --> 00:41:55,050
FAU: As Eugenio reviewed embeds su to representations into SL to see representations, but those can be assembled.
272
00:41:55,560 --> 00:42:08,010
FAU: Into a map from the SU to boundary Hilbert space to the SLC boundary Hilbert space and then the parallel amplitude is just you just take the the SU to loop quantum gravity boundary
273
00:42:08,940 --> 00:42:18,900
FAU: State and you just use the Y map to map it into a an SL to see boundary state and just plug it into the BF amplitude. So it's really coming from
274
00:42:21,780 --> 00:42:24,810
FAU: Obtaining gravity as a constraint BF theory.
275
00:42:27,600 --> 00:42:31,980
FAU: And and so what I want to do is I want to
276
00:42:33,090 --> 00:42:53,520
FAU: Look at the the awesome topics of the of the parallel vertex and understand the geometrical meaning of the critical points that are appearing in the SM tonics by reconstructing the the continuum pull up polonsky to form which will then allow you to reconstruct a continuum.
277
00:42:54,720 --> 00:43:01,500
FAU: tetrad a foreman, and then we can see what how do we interpret these critical points is degenerate versus
278
00:43:03,030 --> 00:43:13,110
FAU: non degenerate and which ones have positive negative orientation. So the meaning of the of the group elements in the group integration is really parallel transports
279
00:43:13,620 --> 00:43:29,370
FAU: From we think of it as from a tetrahedron frame to the force simplex frame. And so in order to assemble the by vectors into a continuum to from, we first have to parallel transport them all to the same frame with the with the group elements and then
280
00:43:30,630 --> 00:43:40,770
FAU: As long as the, the critical point equations are satisfied, there exists a unique to form on the floor simplex considered as a manifold.
281
00:43:42,150 --> 00:43:44,670
FAU: Such that the by vectors are just the integrals of this to form.
282
00:43:46,140 --> 00:44:03,780
FAU: Now there's a caveat here. This is really only true for the for simplex case. But the general for cell case the accounting doesn't work. And so in general, it's not guaranteed that the that the to form will exist, but so I'm focusing on the simply showcase for this part of the talk.
283
00:44:05,040 --> 00:44:07,080
FAU: So I'm
284
00:44:08,400 --> 00:44:09,330
FAU: Yes, so
285
00:44:11,280 --> 00:44:13,710
FAU: The two forms so constructed
286
00:44:14,790 --> 00:44:22,710
FAU: is either going to be of the duel a wedgie form. So the here I the be I'm using here was actually the the dual what Eugenio used
287
00:44:24,510 --> 00:44:28,830
FAU: And in that case, you have a tetrad which has an orientation.
288
00:44:30,000 --> 00:44:46,890
FAU: Or the other possibility is that the the to form is degenerate. So I'm denoting these these cases with a sign omega which defined to be zero. In the degenerate case. And so this table summarizes the the different critical points and
289
00:44:48,420 --> 00:44:59,160
FAU: Which sector, the continuum be falls into it for these different critical points. So in the case of boundary data that fits a Lorenz Ian for simplex
290
00:45:00,060 --> 00:45:11,400
FAU: You have to critical points, corresponding to each of the I read J action and each of the minus i read J action and these corresponds to two different orientations of the tetrad
291
00:45:13,260 --> 00:45:25,290
FAU: There you have a non degenerate tetrad in that case. In the case where it fits a Euclidean for simplex. Actually, what you get is a is a degenerate to form.
292
00:45:26,550 --> 00:45:27,660
FAU: Which is a little bit
293
00:45:29,850 --> 00:45:39,750
FAU: Not intuitive because it would seem that if it fits onto a Euclidean for simplex it's it's not degenerate. But as someone he was pointing out, you can fit together.
294
00:45:41,040 --> 00:45:57,360
FAU: If you can fit together and tetrahedral onto a Euclidean for some flex and you can also fit them together in a flat three plane which is really what's happening here. So these are all degenerate and mission introduce this terminology degenerate type eight degenerate type be
295
00:45:58,980 --> 00:46:10,530
FAU: At someone is request I introduced this first column here it gives another way to understand whether these boundary data corresponds to
296
00:46:11,100 --> 00:46:26,100
FAU: non degenerate or or degenerate for simplicity's using the Kaylee for volume, which as you can see, doesn't really doesn't necessarily fit the categorization here. So there's another way to understand whether these
297
00:46:27,270 --> 00:46:34,290
FAU: Boundary data are degenerate or not, but here I'm I'm focusing on an interpretation which comes from the quantization.
298
00:46:36,210 --> 00:46:37,380
FAU: And the interpreter and the
299
00:46:38,580 --> 00:46:40,710
FAU: Classical correspondence with the discrete variables.
300
00:46:42,750 --> 00:46:44,910
FAU: And the other cases, of course, the vector geometry.
301
00:46:48,060 --> 00:47:00,360
FAU: Let me go back. So that, so the cosine. Problem is, is the is the fact that we're sending over orientations here that you can have both possible orientations and the large spin limit. And then of course we have all these the degenerate sectors and
302
00:47:00,840 --> 00:47:10,680
FAU: The degenerate sectors clearly are not corresponding to something which is gravitational and then there's some debate about whether we should have a be something over orientations.
303
00:47:14,220 --> 00:47:19,680
FAU: The awesome topics can be extended to a general triangulation, which was done by
304
00:47:21,180 --> 00:47:30,600
FAU: Han and Zang. And so what you get is basically you have a some over all possible
305
00:47:31,290 --> 00:47:45,540
FAU: Of these sectors it for each of the for simplicity's independently. So you have a region where it's not degenerate, a region where it's type a degenerate in the region where it's tight be degenerate and within these regions you. Additionally, some over
306
00:47:46,650 --> 00:47:54,900
FAU: Orientations so um so the action that appearing in these topics, if we if we multiply them out, then you
307
00:47:55,890 --> 00:48:02,940
FAU: Then you end up getting an action for the whole amplitude, which involves a sum of all of these actions with signs depending on
308
00:48:03,450 --> 00:48:15,720
FAU: The floor simplex. And this is clearly not the rejection in order to get the red Jay action we would need to not have any degenerate configurations and restrict ourselves to a single orientation or at least not allow the orientation to change.
309
00:48:17,460 --> 00:48:24,120
FAU: And so if we're hoping to obtain gravity by looking at the large spin limit and
310
00:48:24,930 --> 00:48:30,780
FAU: Hoping that the stationary points of that larger than limit or what's going to dominate the path in a row. This is not looking hopeful.
311
00:48:31,290 --> 00:48:44,790
FAU: Because the equations of motion determined by this action or not the equations of motion. And so you're going to have more than just Reggie geometries dominating in the in the large spin limit and
312
00:48:45,870 --> 00:48:56,430
FAU: So you're going to have knowledge of geometry which are which are co dominating which are just as just as as persistent as the equation. So it's not clear that you're really going to get the right
313
00:48:57,570 --> 00:49:02,250
FAU: Some classical limit. And furthermore, these non Reggie configurations are
314
00:49:03,330 --> 00:49:05,550
FAU: suspected to be the source of divergences
315
00:49:07,380 --> 00:49:19,590
FAU: But to understand why the why the these, um, there's some over these different sectors is expected to lead to the divergences it's, there's this work done by
316
00:49:21,090 --> 00:49:33,690
FAU: By Mario's and and others, a while ago looking at the ones on a Reggie model. And there you also have some over orientations for each simplex or neck case there tetrahedral.
317
00:49:35,580 --> 00:49:39,360
FAU: And what you get, again, is an action where
318
00:49:40,830 --> 00:49:43,110
FAU: You have some over lots of different actions where
319
00:49:44,190 --> 00:49:57,600
FAU: The sign is allowed to vary from tetrahedron to tetrahedron. And what this leads to is equations of motion that is not flatness which which which is what you should get into plus one gravity, but a sort of oriented flatness so
320
00:49:58,620 --> 00:50:00,540
FAU: If you define the deficit angle by
321
00:50:03,720 --> 00:50:04,170
FAU: By
322
00:50:06,090 --> 00:50:13,860
FAU: summing over the digital angles weighted with the orientation, then this is what is I should have said this is a two pi, not zero.
323
00:50:15,450 --> 00:50:29,880
FAU: So it's not quite flatness it's some oriented plans. But the point is that this oriented flatness is not the same as flatness because this oriented deficit angle is not deficit angle and a very easy way to see that is that such geometries cannot be symmetrically embedded into our three
324
00:50:30,900 --> 00:50:31,470
FAU: And
325
00:50:32,610 --> 00:50:41,100
FAU: The fact that these configurations can be distinguished from actual flat configurations was pointed out before by these same authors.
326
00:50:44,400 --> 00:50:48,870
FAU: You can see what what what what sort of configurations are allowed. So on the left here, we have
327
00:50:49,350 --> 00:50:54,270
FAU: A flat configuration here I'm visualizing in two dimensions, because it's easier to visualize what's happening, two dimensions.
328
00:50:54,900 --> 00:51:06,480
FAU: And around this hinge. You have no deficit angle. But then as soon as I move this central point outside of the triangle, we have a pocket or a spike and the the
329
00:51:07,050 --> 00:51:15,390
FAU: You have curvature then around the hinge, even though it looks like it's flat, it's not really flat, it's not you have a pocket in there that's not embeddable into a
330
00:51:16,410 --> 00:51:16,980
FAU: Fund space.
331
00:51:19,200 --> 00:51:25,470
FAU: And so the idea is that because these critical configurations are allowed.
332
00:51:27,720 --> 00:51:35,310
FAU: This is actually what's leading to the divergences that appear in the puns on original model because if you just consider for example this
333
00:51:36,570 --> 00:51:42,990
FAU: This this tetrahedron that's been sub divided into four tetrahedral and
334
00:51:44,100 --> 00:51:49,110
FAU: In the, in the path integral, you're going to effectively you're gonna end up integrating over
335
00:51:49,980 --> 00:52:00,120
FAU: The possible positions of this internal vertex and if if you if you really only had the flat configurations which were dominating. This would be a compact integral and you'd
336
00:52:00,810 --> 00:52:14,370
FAU: You'd expect not to have divergences but the point is that because you are allowing these other orientations and these non Reggie configurations. The you, you also have to consider the case where you have the pockets and this. So the central point
337
00:52:16,380 --> 00:52:30,120
FAU: Is gives a critical configuration, no matter where it's placed outside or inside the tetrahedron. So you end up with a divergent integral. And the idea is that this, this can be understood as as the as the source of the divergence is in the hands on original model.
338
00:52:33,660 --> 00:52:45,390
FAU: Another interesting question is, if it's really physical to be something over the orientations, you know and and you there experimentally distinguishable, why haven't we seen any such effects in particle physics experiments.
339
00:52:47,430 --> 00:52:55,950
FAU: Because really it's not just fluctuations that would, that the model would be predicting it would be predicting that these are co dominant contributions to the pathological
340
00:52:57,090 --> 00:53:12,120
FAU: So, yet the dancehall reggae model. It is triangulation independent after regularization, so it seems to be, which is a good indication that it is a correct model of topological theory, like, two plus one gravity, but is it really two plus one gravity. I'm not entirely sure.
341
00:53:15,510 --> 00:53:16,530
FAU: And of course the
342
00:53:17,970 --> 00:53:29,310
FAU: The parallel model has the same issues which you will you will you will only see it for for multiple simplest these these problems arise, but one possible solution that
343
00:53:30,840 --> 00:53:41,430
FAU: I am collaborators proposed some several years ago is the proper vertex, where basically we insert a projector which projects onto the single orientation.
344
00:53:42,510 --> 00:53:44,040
FAU: And enforces a single
345
00:53:45,090 --> 00:53:49,710
FAU: Enforced is not degeneracy with a single orientation and the advantages of this is that
346
00:53:50,730 --> 00:53:52,710
FAU: You no longer have some over orientations.
347
00:53:56,730 --> 00:54:09,210
FAU: All the degenerate configurations are suppressed and so you don't expect the pockets of the spikes. And so, the expectation is that the divergence is will be reduced. You can define it for both Euclidean and Lorenzo and signatures and so far.
348
00:54:10,650 --> 00:54:22,500
FAU: It has the same successful consistency checks and applications to grab the grab on propagator and spend phone cosmology of one major disadvantages that right now. It's only restricted to some initial triangulation.
349
00:54:24,000 --> 00:54:27,450
FAU: It's, it's more complicated than the PR L model so that some
350
00:54:28,680 --> 00:54:35,490
FAU: Some more innovations would be necessary to really do numerical calculations and also
351
00:54:36,060 --> 00:54:45,780
FAU: There's an ambiguity in the definition because you have a choice of where you can insert this projector that's projecting on this one sector, you can insert it at any of the tetrahedron. So what we do is we just
352
00:54:46,170 --> 00:54:52,140
FAU: Insert it in all of the tetrahedron, which one could argue is a bit ad hoc and suggest that maybe there's a there's a better way to do it.
353
00:54:52,740 --> 00:55:06,570
FAU: which avoids that and perhaps even simpler. So what I want to say is that is the proper vertex is is not necessarily the solution, but it's at least a solution to the problem of the some over orientations and and the degenerate sectors.
354
00:55:07,620 --> 00:55:15,960
FAU: And I want to emphasize that. I think it is a. These are problems which needs to be solved. And we will see these problems when we do calculations with multiple for simplicity's
355
00:55:17,310 --> 00:55:20,580
FAU: Another, just to clarify some things about this.
356
00:55:22,470 --> 00:55:32,130
FAU: This idea of restricting to a single orientation was suggested a while ago, in the context of the the Barrett crane model by in this paper by Levine and Ricci
357
00:55:33,720 --> 00:55:34,320
FAU: And
358
00:55:35,340 --> 00:55:37,260
FAU: And they really suggested that
359
00:55:42,120 --> 00:55:55,560
FAU: That if you if you restrict to a single orientation. What you're really defining as a as a causal propagator which is analogous to the fireman propagator and and that actually, in such a case, you don't expect it to.
360
00:55:56,880 --> 00:56:02,040
FAU: To satisfy the equations of motion. So in this sense, you don't expect it to give a
361
00:56:03,090 --> 00:56:08,880
FAU: A projection into solutions to the Hamiltonian constraint, if you restrict to a single orientation.
362
00:56:11,730 --> 00:56:20,550
FAU: But their, their viewpoint, was that both of whether you restrict to a single orientation or not. Both of those possibilities would be useful for different purposes.
363
00:56:22,770 --> 00:56:37,380
FAU: But I wanted to emphasize that in the limiting the sum of orientations. It's much more than just imposing causality. You're not just enforcing that the final state be in the future of the of the past state. There's you're eliminating all these spikes and pockets, which don't
364
00:56:38,610 --> 00:56:47,190
FAU: don't correspond to anything that we see in classical gravity and also there's other work, which suggests that maybe the the
365
00:56:48,150 --> 00:56:58,290
FAU: This something over the orientations is not needed in order to get a projection and solutions and Hamiltonian constraint. In fact, this paper by by Thomas and Antonia actually suggests that
366
00:56:59,550 --> 00:57:11,460
FAU: You need to get rid of the some over orientations, in order to to get a projector into the Hamiltonian constraint. Also in this old work by
367
00:57:12,210 --> 00:57:20,790
FAU: By hurdle and hawking on the no boundary proposal. They're integrating overall Euclidean geometry. So there's no there's no some of our orientations there but yet they still get
368
00:57:22,500 --> 00:57:26,370
FAU: solution. The solution to at least a formal solution to the Hamiltonian constraint.
369
00:57:30,240 --> 00:57:41,700
FAU: So this summer is that of this issue is that there tends to be consensus that the degenerate configurations are problem and are contributing to two divergences but there's
370
00:57:42,420 --> 00:57:47,910
FAU: There isn't consensus from what I find talking to people that the elimination of the cosine
371
00:57:48,810 --> 00:57:59,250
FAU: Is the physical correct thing to do, it does when I do talk to people that there is consensus that elimination of the cosine is likely to reduce divergences it's just not not everyone agrees. If it's the physically correct thing to do.
372
00:58:00,390 --> 00:58:06,540
FAU: And the proper verse vertex eliminates both of these issues above
373
00:58:08,160 --> 00:58:14,310
FAU: But it doesn't mean it's it's the only solution or the best solution, but it's it's the only solution. So, so far.
374
00:58:19,440 --> 00:58:34,320
FAU: So finally I just wanted to make some clarifying remarks on the flatness problem so morning already said some things about this. Here's a brief history of the flatness problem. It was first noticed by Conrad infidel and buns on
375
00:58:35,700 --> 00:58:36,150
FAU: And
376
00:58:37,710 --> 00:58:38,430
FAU: Later.
377
00:58:40,110 --> 00:58:55,710
FAU: Both in near about the same time motion Han and Frank Hellman and what tech Kaminski found that if you're more careful you don't quite get flatness, but you get an accidental curvature constraint. So the gamma times the
378
00:58:58,260 --> 00:58:58,980
FAU: Deficit
379
00:59:00,450 --> 00:59:12,090
FAU: Angle it should be zero module for pie and Hellman and comin comin CD got that it should be modular to pilot, but quite sure what explains the difference of the factor of two. There
380
00:59:13,530 --> 00:59:23,190
FAU: And it should be emphasized that mission pointed out that he didn't. He didn't see this as a problem that actually the deficit angles should be close to zero and the refinement limit. So there's some question about whether
381
00:59:23,730 --> 00:59:31,500
FAU: You know, even if flat configurations do dominate and large spin limit whether, whether that's a problem because maybe the large spin limit is not the right way to
382
00:59:32,550 --> 00:59:34,230
FAU: Consider the semi classical limit.
383
00:59:35,430 --> 00:59:41,580
FAU: There was so all of these were arguing in favor and some sort of flatness, there's another line of argument which tried to show that there was no flatness and
384
00:59:42,750 --> 00:59:50,760
FAU: Which started off with Elena and cloudy. Oh, and 2011 they're the first ones I'm aware of to to use this delta three triangulation.
385
00:59:52,470 --> 00:59:55,680
FAU: To to investigate this question to make concluded that
386
00:59:56,790 --> 01:00:05,190
FAU: That it allows internal curvature, which is not suppressed. But more recently Olivera given more precise version of their argument.
387
01:00:07,470 --> 01:00:14,520
FAU: And the key thing is that it really treating those some over the internal spin something over the internal spin and keeping it
388
01:00:15,150 --> 01:00:26,010
FAU: Discreet not approximating it as continuous. However, there's an oversight, which when correct it actually provides a new argument for that accidental curvature constraint. So this is unpublished
389
01:00:27,780 --> 01:00:31,410
FAU: I mean I guess I shouldn't go into the details, but basically, let me just say that there was
390
01:00:33,060 --> 01:00:52,290
FAU: That there was this imaginary part of the action which Olivera had neglected and when you when you don't neglect it. You, you actually end up getting a the same accidental curvature constraint as as motion haunted and almost telman Kaminski modular this factor of two issue.
391
01:00:53,550 --> 01:00:57,300
FAU: So, but the weaknesses of the of this argument.
392
01:00:58,920 --> 01:01:12,750
FAU: This modified Olivera argument is that first one is taking the large spend some time limit, and then something over internal j is not clear. If this is correct. Also, one is neglecting the dependence of the SEM factor on the internal spin
393
01:01:15,540 --> 01:01:28,620
FAU: And Simone a pointed out that in part of this derivation. One thing that's key to this derivation is is approximating the amplitude in the neighborhood of the critical points.
394
01:01:30,060 --> 01:01:45,330
FAU: The critical points with respect to the the continuous variables. And when you when you when you look at the amplitude and then in the neighborhood. You don't see any evidence of imposition of the closure constraint and shape matching constraints. So
395
01:01:46,530 --> 01:01:59,070
FAU: Which indicates that perhaps these these holes in the arguments are causing the, the key point to be missed the thing which could save you from the flatness of we're not seeing it.
396
01:02:00,060 --> 01:02:10,530
FAU: Perhaps because of these proclamations so so my summary of the of the status of the flatness problem is that every analytical arguments so far. When sufficiently refined
397
01:02:11,010 --> 01:02:21,900
FAU: Yields and XML curvature constraint. However, all of these analytical analytical arguments either have clear holes are are difficult to understand. I haven't wrap my mind around the way front.
398
01:02:22,950 --> 01:02:25,920
FAU: Analysis of filming Kaminski and
399
01:02:27,660 --> 01:02:34,440
FAU: So I really think that the flatness issue is really only going to be settled with numerical calculations and so I'm really excited by all of the
400
01:02:35,730 --> 01:02:42,900
FAU: All the numerical work that's being done in my say. And so I'm hoping that this flatness
401
01:02:44,280 --> 01:02:45,570
FAU: Issue can be settled finally
402
01:02:46,740 --> 01:02:58,410
FAU: And another remark is that even if you do have such a curvature constraint. It doesn't necessarily mean the model is incorrect. But perhaps the semi classical limit needs to include a limit of refinement and which actually deficit angle should approaches you
403
01:03:00,810 --> 01:03:01,380
FAU: And that's
404
01:03:02,820 --> 01:03:05,070
FAU: That's all I had the remark on those issues.
405
01:03:07,410 --> 01:03:11,610
FAU: So I guess we're open for general discussion now in questions.
406
01:03:15,840 --> 01:03:16,740
simone: I think there will be good.
407
01:03:17,190 --> 01:03:17,490
Yes.
408
01:03:19,020 --> 01:03:20,490
simone: For this plenty of topics in
409
01:03:21,030 --> 01:03:29,400
simone: The context of spin for models that we haven't really covered in our presentation. So it's also time for other people to comment.
410
01:03:29,430 --> 01:03:32,250
iPad di Carlo: This is a, this is Carlo can, can you hear me.
411
01:03:34,590 --> 01:03:35,040
simone: Yes.
412
01:03:37,020 --> 01:03:37,590
iPad di Carlo: Okay.
413
01:03:38,790 --> 01:03:40,890
iPad di Carlo: I just want to make a small
414
01:03:42,030 --> 01:03:53,970
iPad di Carlo: Observation is say it's not directly related but it's related to what all you, all you have said this is something that has been new for me. It comes from the numerical calculations.
415
01:03:55,200 --> 01:04:02,340
iPad di Carlo: And I just want to share it. And is this. Um, I've been trying to use the this
416
01:04:03,900 --> 01:04:05,940
iPad di Carlo: Current formulation for doing
417
01:04:07,050 --> 01:04:12,270
iPad di Carlo: Physical calculations in black holes and cosmology and in both cases, it's
418
01:04:13,980 --> 01:04:31,710
iPad di Carlo: You can view it as tried to compute tunneling aptitudes, whether from the contract the universe to expand the universe or from nothing to universal from a black hole tobacco and Francesca Tina has been doing some numerical calculations in for early cosmology and
419
01:04:32,790 --> 01:04:46,950
iPad di Carlo: He has found some some nice expressions that that's not the point. The point is that by looking at the metrics will turn out to be relevant seems to be not the lorente and Reggie geometry. So, but
420
01:04:48,090 --> 01:05:08,310
iPad di Carlo: Some Euclidean so some better job, which is in facts in in in detailing. So this is, this seems to be coming from the numerical. So what I want to say is that, perhaps, of course, quantum mechanics should give us more than the classical limit and
421
01:05:09,510 --> 01:05:20,400
iPad di Carlo: One way of viewing tunneling is that that path integral has some not really subtle points, but some Euclidean subtle, subtle point some some some somewhere else.
422
01:05:21,510 --> 01:05:30,690
iPad di Carlo: That waits into some at any sort of tempting to imagine that this other
423
01:05:32,820 --> 01:05:39,990
iPad di Carlo: The bushes to the amplitude do play a role in the quantum theory and they do play a role in in tunneling. So it might be
424
01:05:41,010 --> 01:05:41,400
iPad di Carlo: That
425
01:05:42,450 --> 01:05:43,620
iPad di Carlo: The quantum theory.
426
01:05:46,320 --> 01:05:56,850
iPad di Carlo: That we have is, is it is Mark is marked. What I'm suggesting is just not let's not just be for opposite to the fact that
427
01:05:59,310 --> 01:06:09,570
iPad di Carlo: In the past will all the classical configuration should come out. In fact, it shouldn't be like that because quantum theory admit tunneling.
428
01:06:10,890 --> 01:06:14,880
iPad di Carlo: This is not a precise point. But I think is an interesting point to keep in mind.
429
01:06:21,480 --> 01:06:30,450
simone: So we haven't yet established at the same classical limit is correct. And there is a risk that the sector vector geometries may cause problems with regards to that.
430
01:06:31,020 --> 01:06:39,630
simone: If it does, then the fact that the sector of actor geometries give some interesting contributions to tunneling, and maybe less relevant so
431
01:06:40,410 --> 01:06:57,600
simone: It's a very nice that they can give some interesting contribution that sense, but we need to make sure that they don't spoil the semi classical limit, I suppose. And then we are free to emphasize these results and like the applications even more I'd see
432
01:07:05,580 --> 01:07:07,050
Eugenio Bianchi: So what
433
01:07:13,980 --> 01:07:18,000
Penn State: One of the reasons why this, we had this panel was because there was
434
01:07:19,860 --> 01:07:39,150
Penn State: No, people are asking kind of rather elementary questions. And so I would like to go back to those elementary questions and I want to thank especially Jonathan more making a nice list of those questions and those questions were a sort of semi classical limit be a flatness problem.
435
01:07:40,500 --> 01:07:40,890
Penn State: And
436
01:07:41,970 --> 01:07:45,630
Penn State: See the issues of divergences and I think
437
01:07:46,860 --> 01:07:54,450
Penn State: Usually a girl very general, you know, all picture, but somehow I didn't see these these problems being directly
438
01:07:55,560 --> 01:08:10,050
Penn State: Answer there and SIMONE IS TALK. I got the impression. And so this is what I want to understand Simone and Eugenio and Jonathan please correct me because we just want to be all on this similar wavelength, even though we may not all understand the technical details.
439
01:08:11,700 --> 01:08:23,340
Penn State: So I got the impression that the issue of divergences is still open and sort of looked at and, in particular, the focus in the numerical simulations, which is very, very valuable.
440
01:08:24,360 --> 01:08:33,840
Penn State: Has been really just restricting was after cases where diversions don't occur. So this point number one. Please afterwards comment on this point number one.
441
01:08:34,830 --> 01:08:43,290
Penn State: And number two, that flat. This problem is still open the arguments, saying that it is flat, but there are wholesome those arguments.
442
01:08:43,860 --> 01:08:55,230
Penn State: And again, Simone and and Jonathan emphasize that. But as what we need is really this numerical simulations, but I'm a little bit confused because I thought that numerical simulations. So far, I mean,
443
01:08:56,190 --> 01:09:06,810
Penn State: There were being performed is restricted context. And I'm not sure that in the near future. I mean, I'm the time scale of a year.
444
01:09:08,070 --> 01:09:17,100
Penn State: That the numerical calculations will be done in the context, which covers all these reservations about the flatness problem. So I would like answer to kind of
445
01:09:17,760 --> 01:09:31,350
Penn State: This thing to do. Second question. And the third question was about this orientation and cosine problem and I mean this has been all these three questions I've been raised by many people. Many times, and I
446
01:09:32,640 --> 01:09:35,790
Penn State: I get I got the impression from Jonathan stock that
447
01:09:37,470 --> 01:09:46,290
Penn State: Unless one really sort of my hand, the requirement that one should just some or one orientation than this problem is there and
448
01:09:47,520 --> 01:09:56,760
Penn State: And more importantly, I felt that he was emphasizing this missions point of view that somehow taking large Jay is not the correct way to take semi classical limit.
449
01:09:57,630 --> 01:10:08,610
Penn State: Now usually emphasize that taking large Jay and resetting gamma to zero size that data and the gamma is finite. Maybe the appropriate way of taking the classical limit.
450
01:10:09,750 --> 01:10:17,220
Penn State: I just let me open a small balances. I think all this discussion is much more much clearer if instead of gamma when he uses the gap.
451
01:10:18,270 --> 01:10:32,700
Penn State: Think of area gap as being independent of GH Barbara plan, plan, so to say. And in other words, if you like the numerical coefficient of the gap. And so what what you're saying is that we've we've sort of lead.
452
01:10:34,260 --> 01:10:47,160
Penn State: Area gap, go to zero j goes to infinity, says the data is finite, but then usually pointed out that there are corrections or daughter of gamma, which is to say correction, daughter of area gap and so quantum geometry which leaves you outside the
453
01:10:48,210 --> 01:10:57,510
Penn State: Other thing. So I'd like to get clarification on all of these three points from the three speakers, because I think it's not just for me. But for many younger people who are asking similar questions.
454
01:11:04,020 --> 01:11:21,240
Penn State: So on the point of flatness, it seems to me there are lots of ideas in a partial proofs on the analytical side. And I understand that this might be feasible, at least, using the data reconfiguration we've been
455
01:11:22,800 --> 01:11:28,890
Penn State: One, maybe two years, one could answer that completely by using metrics.
456
01:11:29,970 --> 01:11:49,620
That requires the definition of what is the problem that is worth formulated even numerically. So in our discussions with john and see Mona. I was proposing something of the kind, because the, the critical point is the flatness award connection or what controversially Sita
457
01:11:51,000 --> 01:12:00,060
Penn State: Spin connection. Is it the actual connection. I see the levee Shibata connection. So one thing that I was proposing is to look for a sunset.
458
01:12:00,870 --> 01:12:19,410
Penn State: For volume in the boundary three volume and defining geometric core machine in those terms one fixes the boundary and then compute the expected value. The for volume. This will give a test of flatness, but they will send the sun is difficult to use know medically
459
01:12:20,880 --> 01:12:22,170
Penn State: The other mark is that
460
01:12:24,090 --> 01:12:42,570
Penn State: Question. So this kind like flatness can be phrased using only few verse disease is factors can be addressed directly numerically. There are other questions, like the one of divergences that they would appear once when, as Steve few, but more vertices at the level of a bubble
461
01:12:43,830 --> 01:12:48,780
Penn State: So there are necessarily one as to truncate the some of the speeds.
462
01:12:49,830 --> 01:12:55,110
Penn State: Either we have a quantum the formation or by and by putting a cutoff and
463
01:12:57,300 --> 01:13:10,650
Penn State: So that makes the medics difficult if one was to see their dependence on our this cut office remote on the other end, if we want to go too many vertices and start testing the behavior of
464
01:13:11,520 --> 01:13:21,840
Penn State: The spin for model we many varieties is to ask all the questions, it seems to me a reason a bola to start looking at locations where the truncation spins is not large.
465
01:13:22,230 --> 01:13:33,360
Penn State: But smaller, possibly as small as he can get for instance only spin 01 alpha where the vertex is purely quantum in the sense of one is not taking any limit.
466
01:13:34,200 --> 01:13:41,910
Penn State: At the level of the single worst x ray starting to ask questions that are genuine genuinely many, many body questions and
467
01:13:42,570 --> 01:13:54,600
Penn State: We have been working on this with Pietro we have a formulation, where are these truncation has done consistently by promoting the Masonic representation representation which gives again.
468
01:13:55,740 --> 01:14:05,130
Penn State: Quantum group the formation as now lambda is not being understood as a cosmological constant something that has to be smaller.
469
01:14:06,780 --> 01:14:13,110
Penn State: Or larger solution scale but campaigns clunky and object. So I think, I think.
470
01:14:14,220 --> 01:14:14,640
Penn State: I think
471
01:14:16,140 --> 01:14:23,940
Penn State: This is something could be explored dramatically and some of the questions are too many businesses. So the second part that you just mentioned.
472
01:14:24,330 --> 01:14:39,000
Penn State: Is it possible that one girl. So look at this many, many words is with small jays to also look at the classical limit question or is that something that for which you you think that large Jesus and James gamma fixed is only way to do it.
473
01:14:40,320 --> 01:14:58,680
Penn State: I think that many vertices. So it's more spins something I want can use us to test the semi classical limit 40 cents in the version where one looks at playing functions of fixed distance. It's boundary distance and from the top and functional one tries to derive an effective action.
474
01:15:00,090 --> 01:15:10,290
Penn State: The value of taking one single verse text and sending it to infinity. I find it still plays an important role because
475
01:15:11,730 --> 01:15:19,470
Penn State: Even when we study spin systems even enough many buddy feces when one study spin system see some valuable to do this.
476
01:15:19,830 --> 01:15:27,180
Penn State: rescaling where what each one of the spins vas has a classical vector and when as a model of the many buddy system.
477
01:15:27,960 --> 01:15:45,720
Penn State: Where each single spin is risky as if it was legit. So I think that there are aspects that there are things that we are learned and we might keep on learning by studying the specific limit. But I don't expect this to be necessary for finding the semi classical Fujimoto
478
01:15:50,910 --> 01:15:59,790
simone: Maybe quickly. Yes. So concerning the first question of a by on the divergence is yes, they can be investigated numerically. It's hard.
479
01:16:00,360 --> 01:16:12,720
simone: The first one that appears as he was shown is my slide is the bubble divergence with to the self energy to for simply says, I don't know. Maybe Peter wants to comment about the feasibility of doing that in the upcoming months.
480
01:16:13,950 --> 01:16:20,850
simone: But yes, you can maybe see the new medically the flatness also as a junior say the delta three is undergoing
481
01:16:21,630 --> 01:16:32,310
simone: Larger strangulations with internal edges as I was mentioning would be the next step that may require one of these super clusters and maybe hopefully we can get access to it.
482
01:16:33,180 --> 01:16:50,130
simone: I as for the semi classical limited there's something that maybe people are forgetting. But these Reggie behavior. Let's not forget it appears of speeds over there 10 to 50 the Laurentian as in politics around somebody did is the worst case he will probably appear 50 to 100
483
01:16:50,460 --> 01:16:51,930
simone: So we're talking about being at
484
01:16:52,110 --> 01:17:01,980
simone: 50 or 100 times the planck length. So it's hard to criticize these as being a gigantic for simplex. So these are edge behavior appears extremely soon.
485
01:17:02,670 --> 01:17:07,800
simone: And considering the same issue. I think the best thing to say is that there really is no consensus.
486
01:17:08,430 --> 01:17:24,420
simone: Even john new genuine myself, even though they do many things on the issue because I don't think we have any clear view in. So I think that's part of the we need more results within more results to get consensus there. That's my view.
487
01:17:25,200 --> 01:17:33,540
Penn State: Thank you very much, so on. So just, again, I just very naive level that particular students and postdocs keep asking if there are, I mean you could
488
01:17:34,320 --> 01:17:48,720
Penn State: Try to calculate those divergent diagrams numerically, but the statement is that they are divergent right and so just calculating the coefficient or something like that numerically. And the question is really values divergent diagrams, then what is our view.
489
01:17:50,010 --> 01:17:52,500
Penn State: Is that we just keep them. What, what, what, what is the point.
490
01:17:53,790 --> 01:17:57,540
iPad di Carlo: Can I, can I comment on this says please
491
01:17:59,040 --> 01:18:08,880
iPad di Carlo: You asked about this three three issues. So let me just give what is, what is the viewpoint about this distribution. So let me briefly summarize the my viewpoint of the three issues. First of all,
492
01:18:10,230 --> 01:18:18,900
iPad di Carlo: The divergence is the the state of the of the theory is that the theorems in which there are no divergences
493
01:18:19,980 --> 01:18:31,560
iPad di Carlo: The several for the version, the quantum deformed version which is much harder to compute with and which has a cut off.
494
01:18:33,030 --> 01:18:41,220
iPad di Carlo: An infrared cut off, which can be interpreted as a cosmological constant. So we always knew that without that
495
01:18:42,990 --> 01:18:45,720
iPad di Carlo: Without that there are these infrared divergences
496
01:18:47,340 --> 01:18:48,510
iPad di Carlo: How do they come in.
497
01:18:49,740 --> 01:18:57,870
iPad di Carlo: In a trap acquisition. How do they wait. I think it's all will be explored and whether they need
498
01:18:59,580 --> 01:19:07,110
iPad di Carlo: They need to grow into my eyes away or whatever. I think I don't have clear ideas. I don't know if anybody else's gear ideas, um,
499
01:19:08,460 --> 01:19:11,970
iPad di Carlo: My hope was that there's a number of things that can be computed the
500
01:19:13,140 --> 01:19:25,170
iPad di Carlo: Like in in quantum field theory before actually going to terms with this infrared divergences come in and this would give us a hint, whether the theories. Interesting.
501
01:19:25,950 --> 01:19:35,430
iPad di Carlo: Already, um, then to address it was just one of the two either the virtual with a quantum group is we're actually what has to go.
502
01:19:36,660 --> 01:19:45,840
iPad di Carlo: Not that the solve the problem. But this at least give us theorems that things are fine it or they have to be normalized in some way. And this is my opinion is open.
503
01:19:47,850 --> 01:19:51,810
iPad di Carlo: And regarding the flatness
504
01:19:53,040 --> 01:19:53,580
iPad di Carlo: Issue.
505
01:19:55,110 --> 01:20:03,180
iPad di Carlo: I am not convinced by these analytical results I find them.
506
01:20:04,770 --> 01:20:08,760
iPad di Carlo: Incomplete and they all seem to miss the
507
01:20:10,440 --> 01:20:13,560
iPad di Carlo: The key detail that intuitively seem to
508
01:20:14,580 --> 01:20:15,810
iPad di Carlo: Suggest that
509
01:20:17,640 --> 01:20:28,050
iPad di Carlo: There's a reason for this to be to be flat. So since I'm anything is complicated. Since the sweetness of jays crucial in this in this sort
510
01:20:29,280 --> 01:20:33,900
iPad di Carlo: What intuitively, what matters is how large is the
511
01:20:36,090 --> 01:20:39,360
iPad di Carlo: How, how large is the bump of the
512
01:20:42,060 --> 01:20:51,810
iPad di Carlo: Around the subtle point because it is really an issue of exchange of limits the limits in which we restrict the integral around the subtle point
513
01:20:53,160 --> 01:20:55,590
iPad di Carlo: Versus the signature itself so
514
01:20:57,150 --> 01:21:03,450
iPad di Carlo: I analytical I'm not able to to give an argument solid argument that make the intuition that this is to be
515
01:21:05,700 --> 01:21:14,340
iPad di Carlo: We try. We have tried to do the numerical calculation in in in in Mercedes since we've tried with this stuff. Seven years ago,
516
01:21:15,660 --> 01:21:16,560
iPad di Carlo: Still with Francois
517
01:21:17,670 --> 01:21:27,120
iPad di Carlo: I think we're moving toward that. And I hope this is a very good nice problem it's it's relatively clear
518
01:21:28,740 --> 01:21:37,800
iPad di Carlo: And it will be solved, and I agree with Daniel that once you be careful in interpreting things and asked, What exactly
519
01:21:39,840 --> 01:21:55,080
iPad di Carlo: Are we asking to the theory, we might be confused. The interpreting this data us curvature that might be one of the sources of the of the question. So the real question here is whether we get the classical limits. Correct.
520
01:21:56,520 --> 01:22:03,360
iPad di Carlo: In a situation in which there is a too complex where we expect to be curvature inside so
521
01:22:04,770 --> 01:22:05,220
iPad di Carlo: Let's
522
01:22:06,480 --> 01:22:18,180
iPad di Carlo: address the question halfway through this is the right question. And I think it will be solved with sufficient effort. The third question is about the cosine
523
01:22:19,200 --> 01:22:24,150
iPad di Carlo: I agree there's no consensus there. There's definitely a positive always be no consensus, I expect
524
01:22:25,440 --> 01:22:28,830
iPad di Carlo: The, the, the, the, the amplitude to have both terms.
525
01:22:30,660 --> 01:22:41,700
iPad di Carlo: I think it has to have both terms because the winner. David equation is real, because that would be expect from the theory. This is not defined by the exponential of the
526
01:22:43,350 --> 01:22:44,280
iPad di Carlo: Of the
527
01:22:46,650 --> 01:22:48,540
iPad di Carlo: AI the classical option.
528
01:22:50,340 --> 01:22:58,890
iPad di Carlo: These are just type. What is it I find an eight arguments like oh, but then we should see physically
529
01:22:59,970 --> 01:23:03,390
iPad di Carlo: Some physical effect of the other term.
530
01:23:05,040 --> 01:23:05,460
iPad di Carlo: Tweet.
531
01:23:06,720 --> 01:23:21,420
iPad di Carlo: And not not found it. I think that OTT and even had a point is saying the quantities in in in fuel theory, though, to kind of propagate those one that propagates ahead and went propagates ahead and back.
532
01:23:22,530 --> 01:23:25,410
iPad di Carlo: The the the
533
01:23:26,520 --> 01:23:29,070
iPad di Carlo: Spin form includes
534
01:23:30,180 --> 01:23:41,220
iPad di Carlo: Both of them. Now let me be clear, this is not a reason for thinking that what john does is not interesting mainly his considerations are interesting.
535
01:23:41,670 --> 01:23:49,140
iPad di Carlo: As a motivation to explore something else as a motivation to expose anything else. Very well. So if there's another theory.
536
01:23:49,950 --> 01:24:02,010
iPad di Carlo: With a proper vertex that works fantastic but they don't think their motivations are strong enough to doubt that without it, it might be, it might give them the classical limit. Correct. Nevertheless,
537
01:24:03,540 --> 01:24:12,330
iPad di Carlo: So I worry much more for how we will be able to control the divergences
538
01:24:13,530 --> 01:24:13,950
iPad di Carlo: And
539
01:24:16,620 --> 01:24:18,900
iPad di Carlo: How this will affect calculations.
540
01:24:19,980 --> 01:24:20,610
iPad di Carlo: Then
541
01:24:22,470 --> 01:24:40,320
iPad di Carlo: Then a priori arguments, this should be wrong. And I think that this is going to be tested by using this, not by keep going around in a circle on on abstract arguments. So once we can compute something suddenly things will become much more clear.
542
01:24:42,000 --> 01:24:49,590
Penn State: That's it. Okay, thank you very much and I can know that that was very helpful. There are people in API, who I think are strong views about
543
01:24:50,490 --> 01:25:01,230
Penn State: The issues and limitations and I hope that they can speak up so that I think everybody kind of comes to the same on the same wavelength. Can people in ti please pick up
544
01:25:28,860 --> 01:25:35,280
Marseille: While we wait for people to wrap up their mind if they want to intervene. Maybe I can address
545
01:25:36,450 --> 01:25:48,690
Marseille: A couple of points in response to a bias question and try to specify a little bit more what Simoni was saying. So about the nomadic so in particular.
546
01:25:50,190 --> 01:25:51,210
Marseille: The nomadic say
547
01:25:52,410 --> 01:26:00,570
Marseille: We have a code that works very well for one vertex diagram the code works also for
548
01:26:02,760 --> 01:26:06,270
Marseille: Two or three vertices diagrams in particular.
549
01:26:08,100 --> 01:26:13,860
Marseille: divergences as being computed the within BF beauty and
550
01:26:13,950 --> 01:26:23,670
simone: Center. Once they got john, can you stop sharing the screen so I can show the vertex diagram that Peter is talking about. Go ahead, Peter. Sorry. So
551
01:26:23,880 --> 01:26:28,080
Marseille: The vertices has been completed numerically for BST.
552
01:26:29,250 --> 01:26:52,740
Marseille: In three and four dimension by three and four dimension. I mean, using vertices that are four and five, Ireland and they both the verge as they should be, because the computation can be also done analytically. Exactly. Then the computation of the agencies that I perform the
553
01:26:54,510 --> 01:27:02,130
Marseille: Art regarding the diagram on the left, so it's our if you wanted some time or the for the epl
554
01:27:03,270 --> 01:27:03,750
Full
555
01:27:05,370 --> 01:27:06,240
Purity
556
01:27:07,320 --> 01:27:17,550
Marseille: Where they just so they're the group is a sad to see. So it's burdensome. But then restricting to football in vertices. And for those kind of
557
01:27:19,980 --> 01:27:24,270
Marseille: Theory, I was able to complete that diagram and that diagram is not divergent
558
01:27:25,410 --> 01:27:26,280
Marseille: What but
559
01:27:27,720 --> 01:27:32,640
Marseille: Then for the full four dimensional theory. The one on the right.
560
01:27:33,990 --> 01:27:43,710
Marseille: Was not able to perform the numerical evaluation, but I was able to use nomadic estimate
561
01:27:44,820 --> 01:27:56,880
Marseille: Our love for the single components forming their the amplitude and there was able to estimate the divergence of the diagram but just growing together informations
562
01:27:58,890 --> 01:28:04,770
Marseille: So I don't have numerical computation of the fully p&l
563
01:28:06,180 --> 01:28:08,520
Marseille: Model that merges, if that's the question.
564
01:28:09,540 --> 01:28:17,850
Marseille: But I still expect the divergent and then about flatness was what's the status for
565
01:28:19,140 --> 01:28:35,520
Marseille: The medical study of the flatness problem. And here I can be very concise and precise. I will say that yes we're focusing on this that the 3D English we perform the first as very acts.
566
01:28:36,660 --> 01:28:38,490
Marseille: As an exploratory work.
567
01:28:39,600 --> 01:28:42,960
Marseille: We explored the case of
568
01:28:44,790 --> 01:28:59,610
Marseille: The three damnation. The concert at your mother just to understand what we need for then we are they be performed. But he still unpublished and to be polished the
569
01:29:00,690 --> 01:29:16,740
Marseille: Computation in the for the that the three k's in fourth dimension STD STD, and we add the code ready to run for the delta three and in the epl for the API model.
570
01:29:18,000 --> 01:29:19,020
Marseille: However,
571
01:29:20,040 --> 01:29:24,840
Marseille: There's a little bit more work still needs to be done and
572
01:29:26,370 --> 01:29:33,870
Marseille: Some German German geometrical inputs. For example, we, we still need to define the
573
01:29:35,190 --> 01:29:37,200
Marseille: Boundary data precisely
574
01:29:40,050 --> 01:29:53,220
Marseille: And just to add that one last problem. So the complication with the new metrics is not really in the number of vertices, but his modem, the number of internal feces.
575
01:29:54,240 --> 01:30:02,100
Marseille: And yes, apart from the metrics or the cases we looked at for women are just
576
01:30:03,150 --> 01:30:05,370
Marseille: Bonded internal feces so that
577
01:30:09,570 --> 01:30:15,390
Penn State: Thank you very much. So in this case, for example, for the delta three calculation. I just want to understand the viewpoint.
578
01:30:15,990 --> 01:30:26,040
Penn State: Supposing this one calculation showed that it is, in fact, that then would you would the point of view would be a while. But yes, but that is too simple, and we should look at more complicated configurations
579
01:30:27,000 --> 01:30:40,800
Penn State: And conversely, if we found that in this configuration. It is not flat would one then say that, well, if it's not flat already so therefore it will not be a flat elsewhere. What kind of is a viewpoint about
580
01:30:43,020 --> 01:30:45,090
Marseille: So, here there are two questions.
581
01:30:50,790 --> 01:30:52,950
Marseille: Curve geometries allowed them second
582
01:30:55,980 --> 01:30:57,390
Marseille: Semi classical of
583
01:30:58,980 --> 01:31:10,260
Marseille: The model the right one. So, for the third first question, I think. Yes, that that the three and not the analysis of the parallel to the in the free
584
01:31:12,210 --> 01:31:16,710
Marseille: Triangulation will be announcer for the second question.
585
01:31:17,730 --> 01:31:19,470
Marseille: I would say no, it's not an answer.
586
01:31:23,670 --> 01:31:29,610
Penn State: Right. But the first question. If you are equal to zero. Would you not say that. Well, yes, it is zero, but that is because this is
587
01:31:30,180 --> 01:31:42,630
Penn State: Our special configuration and therefore not. In other words, if you found that it is non zero, then it will be an answer, but if it is zero, then you will not really even answer is not your viewpoint. I'm just trying to understand the viewpoint, so
588
01:31:43,140 --> 01:31:43,620
simone: Yes, yes.
589
01:31:44,160 --> 01:31:58,890
simone: Yes, yes, it's a non trivial test. So if he fails it. That's kind of definitive in the negative. But if he passes eater, you can still check for more or less reveal tests. So yes, the answer your question is yes. Yeah.
590
01:32:02,970 --> 01:32:06,690
Hal: This is how a bard two quick comments.
591
01:32:09,030 --> 01:32:27,180
Hal: Just connecting things that there was a request from the viewpoint for PCI, and there are a couple of things I can comment on there so Carlos mentioned the the quantum defamation. The queue defamation and the, the capacity for that to to regularize the divergences
592
01:32:28,320 --> 01:32:49,110
Hal: And mission and vojtech and outdoor retailer and I worked on this and we worked on in particular on a complex assignments theory approach. And in that context, you, you do seem to get this regular rate regulation of the divergence is we studied at a single vertex level.
593
01:32:50,310 --> 01:33:00,780
Hal: And and it's interestingly what we find is that you have to fatten your spin networks. So you have to go to a tubular neighborhood of the spin network.
594
01:33:01,350 --> 01:33:08,310
Hal: And it seems to me this connects with the recent work of Danielle aprons at the at the Levine and they're on Friday.
595
01:33:08,550 --> 01:33:24,840
Hal: Where they're studying an extension of the cemeteries on spin networks to sort of conquer asymmetry, instead of just Lawrence group symmetry, where they're also finding fat and spin networks. So there's an interesting connection there between the cemetery algebra.
596
01:33:25,890 --> 01:33:31,230
Hal: The charges of the theory and and this regulation of divergence is
597
01:33:32,850 --> 01:33:35,940
Hal: Second comment in a totally different line.
598
01:33:37,080 --> 01:33:44,760
Hal: BIANCA Dietrich and Seth, a song and I have been thinking a lot about area calculus recently area, Reggie calculus.
599
01:33:45,330 --> 01:33:53,310
Hal: And in particular, we've been going in this direction that Simone Simone. A was pointing towards thinking about area angle Reggie calculus.
600
01:33:53,820 --> 01:34:03,930
Hal: And the hope is to better understand the gluing even at the classical level and then to try to character I spend from models by how your
601
01:34:04,380 --> 01:34:23,340
Hal: How your gluing is imposed. So if I take two for simplicity's like glue them along a tetrahedron. I could imagine trying to take a coherent state for that tetrahedron and perfectly glue them or I can relax that gluing and try to understand what's going on. So we've been very much
602
01:34:23,760 --> 01:34:24,990
Hal: going in this direction. So Monday.
603
01:34:24,990 --> 01:34:31,230
Hal: was mentioning of trying to understand better what all the conditions that come out of a certain model me
604
01:34:51,270 --> 01:34:55,650
pullin: Okay. So are there other outstanding issues or should we start thinking about wrapping this up.
605
01:34:58,620 --> 01:35:08,550
FAU: I just wanted to make our mark that I agree with with with Carlo that these issues are going to be settled when we actually do calculations of physically relevant things and
606
01:35:10,530 --> 01:35:16,500
FAU: I mean there's there's some, there's some hope or expectation that the proper vertex might
607
01:35:17,640 --> 01:35:22,230
FAU: Get rid of that divergence is also but that's something that hasn't been tested yet. It's something I'd like to do
608
01:35:23,280 --> 01:35:28,530
FAU: Sometime soon, but there are definitely a paths forward and in different directions.
609
01:35:36,390 --> 01:35:39,570
Penn State: Yeah, I think we can wrap up. It has been already
610
01:35:40,770 --> 01:35:41,310
Penn State: Like later.
611
01:35:42,030 --> 01:35:43,770
pullin: Okay, so let's thank the speakers.