0 00:00:05,609 --> 00:00:16,440 Okay, then let's start. Hello everyone, to The Curious all scheduled today's speakers younger DT with quantum geometry from higher gauge theories 1 00:00:18,210 --> 00:00:28,680 Thank you everyone for tuning in. So I will speak about this part of geometry form if he and I should think my key and so on and we'll 2 00:00:29,910 --> 00:00:33,390 For actually organizing a quantum repeater last window. 3 00:00:34,860 --> 00:00:44,130 And they put together some people into reading books. And so this is one of these open loops this this people which appeared in August. 4 00:00:45,990 --> 00:00:51,720 And it's basically weapon by my muscles open book, and as I will explain. It's about 5 00:00:53,490 --> 00:01:02,280 Extending he retired he read and getting some very interesting lessons for point of view on it and it candidate for quantum geometry out of it. 6 00:01:05,250 --> 00:01:07,320 So the main message will be that this 7 00:01:09,240 --> 00:01:15,120 prospect for new for the quantum geometry which will include 8 00:01:16,230 --> 00:01:16,470 Us. 9 00:01:19,770 --> 00:01:20,460 Listen, okay. 10 00:01:23,280 --> 00:01:23,700 Hello. 11 00:01:27,300 --> 00:01:28,380 Can anybody hear me. 12 00:01:30,840 --> 00:01:32,130 Yes, we can hear you fine. 13 00:01:32,550 --> 00:01:32,970 Yes. 14 00:01:35,280 --> 00:01:47,010 Okay so includes Edwards as as basic many units are supposed to just be vectors and the recon you get the momentum. And that's the two connection which 15 00:01:47,640 --> 00:01:58,200 If the need to the higher THC. So it's a two page Siri, and there's two connection will be a to phone so if you form the two curvature. It really ski form. 16 00:01:58,860 --> 00:02:11,970 And it turns out that the sleep on us as a spacetime different often generator for for the tech bytes, particularly, it really does immediately generate the Nordics translations. 17 00:02:13,920 --> 00:02:21,630 And to Siri, as opposed to consideration of the edges which is done by the just the user curvature and be absolutely 18 00:02:23,280 --> 00:02:30,840 So, it offers many advantages on the kinematic and dynamic level and we will see that we already learn one lesson about 19 00:02:31,860 --> 00:02:35,010 The dynamic content of quantum gravity. 20 00:02:37,830 --> 00:02:41,220 So here's an overview of my talk, a try to give a very fast. 21 00:02:42,450 --> 00:02:52,680 If you have sweetie quantum reality and see how nicely things look to see maybe them to compare to 40 quantum gravity. 22 00:02:54,270 --> 00:03:03,510 And this will be based on like to acknowledge the configuration space. And I would argue that maybe 40 we should actually a notch more than we usually do. 23 00:03:04,650 --> 00:03:08,340 And this would be basically based on the BSC G action. 24 00:03:09,510 --> 00:03:24,120 And then I represent a bit what we actually did. And the people that would be the quantization also section. The I think the spin bobin order and quantum geography and the closest an Outlook. So for all people expected 25 00:03:25,830 --> 00:03:31,770 And introduction for two categories and release every almost no to category. 26 00:03:32,910 --> 00:03:43,500 Descriptions appearing here. So it's mostly based on on geometrical insights, which actually indeed help us to solve a problem in society. He 27 00:03:44,730 --> 00:03:45,690 Context. 28 00:03:47,010 --> 00:03:53,070 So let's start with the CV gravity. Imagine we do a positive good see veggie I close 29 00:03:54,330 --> 00:04:02,820 The water. Start with a triangulation attach some legs very evil to the edges and try to define or to compute as possible. 30 00:04:03,600 --> 00:04:14,610 Now the actually be a very complicated function on polynomial legs for earbuds. Additionally, you have to worry about the domain of integration because they will be 31 00:04:15,720 --> 00:04:18,300 tying it in the qualities and inequality. 32 00:04:19,680 --> 00:04:22,980 And so on. So you get some complicated constraints. 33 00:04:25,410 --> 00:04:30,750 The trick here is to enlarge configuration Spain's space and then to contain again. 34 00:04:32,220 --> 00:04:35,730 And particular to introduce clients. 35 00:04:36,870 --> 00:04:47,790 So that when since I'm a clickable have some positivity properties. And in this case, Google, it was a first order formulation and introduce an independent spin connection. 36 00:04:49,050 --> 00:04:55,050 So we were introduced to gauge freedom and just needs to support any action. 37 00:04:56,730 --> 00:05:05,730 And one except also be affection and as you can see the Palestinian action is just Ninian's tired fields. 38 00:05:06,780 --> 00:05:26,310 So if you'd like to ask them to go to the actual listen I we can integrate out I feared and VCs are basically this Thai food. Excellent. Thanks, Mike. Much don't have to impose anything curvature. So what we end this is 39 00:05:27,630 --> 00:05:32,070 Also be going for for quantum gravity and really it's just the positive 40 00:05:35,970 --> 00:05:44,010 Actions and this we should idolize Francis some lettuce and so he gets a presentation of 41 00:05:45,180 --> 00:05:47,160 Authenticity authentically in 42 00:05:48,300 --> 00:05:49,590 Any event on hollowness 43 00:05:51,510 --> 00:06:02,760 Now, what we use on a technical level is appropriate one form. So we expand functions in this case a data function over group element. 44 00:06:04,380 --> 00:06:19,500 To be a representation in business and use various states and so on. And then end up Miss upon sandwiches order which he is just within the tetrahedron people left out signs of dementia factors and so on. 45 00:06:20,550 --> 00:06:31,170 So we get to this loop a positive. So we just assign it to eat all get to six seasons, which automatically satisfy all this time and any qualities 46 00:06:32,370 --> 00:06:33,120 Associated with that. 47 00:06:36,300 --> 00:06:43,500 And, you know, was actually invented in 68 based on a completely different arguments. 48 00:06:45,870 --> 00:06:51,780 And this gives you a very reasonable TV quantum gravity Siri, which unfortunately is still a bit 49 00:06:52,890 --> 00:06:57,060 unappreciated to can make it very defined of the vaccine. 50 00:06:58,440 --> 00:07:15,660 There's lots of work which teaches that you can even understand if you do symmetry and consistent Hamiltonian aijalon could say algebra. In this model, and this is me audience and the different multiple constantly translates vertices 51 00:07:16,680 --> 00:07:19,410 Into hyper surface triangulation, and this case. 52 00:07:20,970 --> 00:07:22,800 We know that canonical quantization. 53 00:07:24,120 --> 00:07:32,820 Can choose canonical quantization. So that's experiment positively quantization. One can also show equivalents to transfer payments and so on. 54 00:07:35,640 --> 00:07:41,850 So the recent calculation, which we have done is to define all the classic toys or find the boundaries. 55 00:07:42,240 --> 00:07:48,930 And if you take the limit and as opposed to kind of limit you actually even was be speaking collectors for this petition function. 56 00:07:49,710 --> 00:08:05,400 And this was a calculation, which has been done first and affirmative duty, so you can immediately make you can actually make contact with petabyte of pitino calculations. This is Facebook, of course, he has open fashions these questions. 57 00:08:07,080 --> 00:08:22,470 They put into two sessions about what on what does one understand our theory of functionality. So make sure you could ask this, this model invoice some orientations. There was a widening numbers, which also show up in this 58 00:08:23,820 --> 00:08:34,650 In this example of the BMS we can come into should say busy no should say not busy and so on, but otherwise it's a completely consistent quantization of sitting 59 00:08:39,870 --> 00:08:50,130 On the canonical side us one we can lie to Connecticut a bit space and place the network functions and you can define all this quantum jump up are believers. 60 00:08:51,030 --> 00:08:58,470 And this also part of an ISIS formal quantization of lettuce a space which is given by associating 61 00:08:59,430 --> 00:09:16,110 He started as a tool which comes with some slight exception to each link. So one copy of this is equal to each link now becomes a very important point. So this link actually represents that instruction, the sense that 62 00:09:17,460 --> 00:09:28,410 We, the subject expansion sounds like the title to get to the enemies and to tie it is me it over the edges of the emulation something one dimension. 63 00:09:29,040 --> 00:09:37,200 So, hello. Nice. Nice. Almost meeting or connection over one dimension and actually is doing. So it's also something one dimensional 64 00:09:37,830 --> 00:09:53,430 So here we have a situation where, basically, these two variables us me the way each one dimension and one plus one is two. It gives us the space, the dimension of space. And that's important to get us a subject exception to get the big mountain, you can 65 00:09:54,480 --> 00:09:58,140 Sometimes matrix or measure independent syntactic structure. 66 00:09:59,940 --> 00:10:09,720 And as we'll see in four dimensions and we need to get see on the right hand side and then we need to decide how to split this into two plus one one plus two. 67 00:10:12,030 --> 00:10:21,210 So let's look at 4070. Can we do a symmetric. So there's a first order formulation based on the quality action which is nonlinear and templates. 68 00:10:23,340 --> 00:10:25,620 We have to be affection, which is topological 69 00:10:26,640 --> 00:10:28,080 And maybe it's a true form. 70 00:10:29,730 --> 00:10:43,620 And of course we know that to get really gravity would have to add constraints to the SPF action and if it's a pretty ballsy action resist constraints and for simplicity of the two 71 00:10:44,940 --> 00:10:48,810 So to form field to lies on a very 72 00:10:50,610 --> 00:11:04,320 Of course we know also that, in this context, the simplicity constraints aquatic oneself more cycles. I don't comment on that. So one of these sectors is this one here is a geometric sector. 73 00:11:05,970 --> 00:11:23,370 Interestingly, these different formulations. So as a BF actions that have been ski action then Apollo teeny action if you add to hold stone to it and the Africa by be able formulation already to similar space and to open up a similar kind of quantum geometry. 74 00:11:26,850 --> 00:11:27,810 So you 75 00:11:29,400 --> 00:11:37,320 Go now to the CD hyper surface and sip as one and you triangulate and again to each when 76 00:11:38,760 --> 00:11:47,130 You associate a copy for instance of these ties it all if you're already in time gauge and so on, or if you are not scared. 77 00:11:48,210 --> 00:11:49,500 Of the style. So, for 78 00:11:51,360 --> 00:11:52,470 In this case, 79 00:11:54,180 --> 00:12:09,390 The variables which are connected to each other one I quality a bee bee. So before, so he feared and he encodes knowledge was a triangle. So it's based on devices form. 80 00:12:11,010 --> 00:12:20,790 This meeting was applying and so hold on me. It's coming again from the integral was a link. So again, they have a conjugate appeal. 81 00:12:21,630 --> 00:12:33,390 But this time, we need really to integrate one of these barriers and really be in this case was something two dimensional because in the end be meter that is dimension at up to see 82 00:12:39,030 --> 00:12:44,640 So from from this be like door to funkier so from be we 83 00:12:45,810 --> 00:12:49,170 Usually would deconstruct the pilot 84 00:12:52,230 --> 00:12:54,600 And then you can complete a new template. 85 00:12:57,030 --> 00:12:59,190 Was this problem. 86 00:13:01,290 --> 00:13:09,360 On issue if you want. And because if one the concert series hide from one template and the tides for another 87 00:13:11,340 --> 00:13:23,400 One notices that shape sheep have two triangles, which one would like to identify actually do not match the time as much but the kinds of shapes, do not match. 88 00:13:24,480 --> 00:13:24,900 And 89 00:13:26,160 --> 00:13:27,360 I think the notice it. 90 00:13:28,470 --> 00:13:32,640 In the canonical formalism first though with James I know 2008 91 00:13:33,960 --> 00:13:40,020 And these constraints actually appeared before on the similar in 2007 92 00:13:43,200 --> 00:13:49,290 So be there, but the supplies exam because we expected. That'd be fine. Really, Reggie, some tissue geometry. 93 00:13:52,020 --> 00:14:02,640 Um, but now it's a very known fact and effect was one motivation for calling the local remedy geometries with the geometries. 94 00:14:05,220 --> 00:14:09,150 Later we found out that that will be important point is 95 00:14:10,260 --> 00:14:18,810 That this is an argument of office space of geometry advisors to due to the fact that 96 00:14:20,490 --> 00:14:25,590 Certain height of constraints which we need edge simplicity constraints are not imposed. 97 00:14:26,610 --> 00:14:32,490 So these edge Simplicity Simplicity constraints, the month following. If you will reconstruct 98 00:14:33,600 --> 00:14:48,210 For instance, a tired from your beef fields and to transport this diet, which is associated to get an edge and I want to actually say if you wanted this tight Victoria stable analysis on me. 99 00:14:49,350 --> 00:14:52,440 So actually this this constraint. 100 00:14:53,730 --> 00:15:07,080 Is equivalent to the secondary simplicity constrained and the secondary simplicity constraints I proven to the reality conditions on the African connection and effect. It's also a property of a display which will be a connection. 101 00:15:08,490 --> 00:15:18,810 And actually later we will see that this constraint is actually considered as a disk utilization also offers a first BMP identity. 102 00:15:20,490 --> 00:15:25,380 Which comes from basically that the conditions that portion vanishes. 103 00:15:26,610 --> 00:15:27,270 Um, 104 00:15:32,100 --> 00:15:44,220 There was some discussion about the interpretation of the ICO later. Again, we will really see that you can identify that this some kind of fortunate degrees of freedom is still ongoing discussion with this. 105 00:15:45,690 --> 00:15:46,440 This issue. 106 00:15:47,730 --> 00:15:57,960 Isn't it's a problem for the spin form and a pudgy dynamics. So for me that was always a question, what do we do with this and notched face face of geometries. 107 00:15:59,160 --> 00:16:08,940 I can also ask this question, it's been foam and one person which which pointed out that order forms the beginning, maybe also the Alexander 108 00:16:10,770 --> 00:16:18,810 Was also built by Simone and answer. How about ocean. How should be defined the dynamics on this extended face face. 109 00:16:22,080 --> 00:16:26,670 So basically, for me, it was, it goes back to suspected want us to see 110 00:16:27,810 --> 00:16:39,270 Because if you want to gauge formulation. So you really want is a whole other means, which was near the world war one I mentioned things that will links and then 111 00:16:40,410 --> 00:16:48,090 You get us going to get it very that's something which is defined as a to form. And so this as a director feuds 112 00:16:52,050 --> 00:16:52,440 And 113 00:16:53,490 --> 00:17:06,360 We say import users extend the curvature. There's a star. It's actually the curvature, because, in fact, it says, which has anybody find if you have actually uniquely construction of the pilots. 114 00:17:07,380 --> 00:17:22,770 Which allows you then to reconstruct the lever to be the connection effect as we have seen the edge simplicity constraints is about having a very defined he beat up on action. And so if that's not possible, you accept the curvature is a biggest 115 00:17:24,570 --> 00:17:28,140 And the beef years unquote areas moments to find it. 116 00:17:29,460 --> 00:17:32,910 And furthermore, if you if you really look at BF 117 00:17:34,320 --> 00:17:36,840 Dynamics. This is based on 118 00:17:38,070 --> 00:17:52,590 On the consented to banish it's a to form and as a to form a basically can see only edges can see one dimensional objects. And in fact, it generates edge translations instead of vertical stations. 119 00:17:53,760 --> 00:18:03,210 And there's an auto proposal by Republicans upon which proposals to break this excellence Asian cemetery don't have an explanation. 120 00:18:03,810 --> 00:18:14,400 If you think about it, what was I didn't know nope expressions nonetheless it's, it's, it's an interesting proposal which, to my knowledge, unfortunately, nobody really followed up this 121 00:18:15,240 --> 00:18:26,760 And the more modern incarnation of the Hamiltonian contains actions sections actually based on paper Edo over to my opinion has a disadvantage because you lose of it's a geometric interpretation. 122 00:18:28,470 --> 00:18:29,970 Say virtue and virtue paperless 123 00:18:31,110 --> 00:18:34,230 Hamiltonian constraints generate erotics translation. 124 00:18:36,660 --> 00:18:49,140 If you have an action based on paper, you know, I'm Penn State my heat and your hypothesis, it should actually also like a long object. So you would expect the kind of fun. Okay. 125 00:18:53,400 --> 00:19:03,420 So what one actually what like this to a place to be fields which are based on time. Is this 126 00:19:05,820 --> 00:19:06,780 One forms. 127 00:19:09,060 --> 00:19:10,380 To really get 128 00:19:12,900 --> 00:19:14,040 The Matrix geometry. 129 00:19:16,320 --> 00:19:19,800 But since the titles are one forms, it would miss one dimension. 130 00:19:21,750 --> 00:19:28,680 In fact, if you look at the canonical analysis of the votes, the monkey action we do saw this one phones but then 131 00:19:30,270 --> 00:19:31,170 We find that 132 00:19:32,820 --> 00:19:35,160 It's very connected to the 133 00:19:37,470 --> 00:19:39,720 Connection is actually 134 00:19:41,070 --> 00:19:43,740 So energized and most 135 00:19:45,840 --> 00:19:48,540 Of these one forms and that leads us to the to form. 136 00:19:53,490 --> 00:20:00,750 So here what what this proposes to again applies a strict and a notch. The space and then constraining in 137 00:20:04,050 --> 00:20:09,210 This announcement proposes to introduce actually to form. 138 00:20:11,220 --> 00:20:12,630 Which is a connection. 139 00:20:13,830 --> 00:20:24,300 And since the now. Oh, from one connection form poor to connection for it, we are free to choose to either templates. 140 00:20:25,620 --> 00:20:27,030 As the quantity editable. 141 00:20:28,770 --> 00:20:35,460 And so we use it. Not only is one plus to see, but also the two plus one is St. So it's a very natural. 142 00:20:36,480 --> 00:20:37,200 Allotment 143 00:20:39,090 --> 00:21:00,750 So notice that I chose here the connection and the be fields. So for that, you'd be choose the to form and pilots templates to be are for valued and that will have a specific reason. And the reason is that they want to fit into this to gauge theory, which I will explain on the next slide. 144 00:21:04,650 --> 00:21:13,770 So later we can imagine that we actually want Spain's of leaders and the connection one form and have nots will be a will basically 145 00:21:14,850 --> 00:21:19,320 Be feared and the connections will be expressed in terms of establishments. 146 00:21:21,960 --> 00:21:26,250 Let me introduce one quantity which is to curvature 147 00:21:27,330 --> 00:21:30,720 To cook curvature is defined as a call and 148 00:21:32,970 --> 00:21:35,160 Also to have some connection. 149 00:21:36,510 --> 00:21:38,490 And this would be a sequel. 150 00:21:40,980 --> 00:21:47,490 So you can ask no Uzi study this come from some actual question. Yeah. 151 00:21:48,210 --> 00:21:55,200 Is churchy variable really something like a proxy for the tourism Stevie wedgie me 152 00:21:57,480 --> 00:22:03,900 Given up. He is a portion of the video almost see it on the next slide and two seconds. 153 00:22:10,920 --> 00:22:18,000 So, but it comes from an action and that is a BSc G action which was defined by what we own 154 00:22:19,710 --> 00:22:25,650 And like 500,000 in preventable and 2007 155 00:22:27,510 --> 00:22:35,040 And you can all contemplate why it's called a BSc G action, given that existed a b f x 156 00:22:36,750 --> 00:22:37,860 Y you complete it. 157 00:22:39,060 --> 00:22:49,980 Contemplated it will renamed the HCG action to a BF eg action. So, this we will actually identifying the CPS with atheists. 158 00:22:51,690 --> 00:22:56,370 Now remember that G was Jessica derivative of this to connection. 159 00:22:57,690 --> 00:23:01,320 I think so. It depends on the one connection and on the connection. 160 00:23:02,370 --> 00:23:04,500 And if you do an integration by parts. 161 00:23:06,870 --> 00:23:13,050 In fact what appears is an older when the limit of x on the 162 00:23:14,310 --> 00:23:16,950 Fields and that'd be fine to the torsion. 163 00:23:18,960 --> 00:23:25,680 So, yet the action of basically BF C D can understand us 164 00:23:27,450 --> 00:23:30,000 An action for enforcing to constraints here. 165 00:23:31,050 --> 00:23:36,330 One is a one curvature constraints, until eventually the player is be 166 00:23:37,770 --> 00:23:49,800 On the second part, we have a choice. We choose here that the single to torsion as a constraint. So we have supported on saying answer to connection very acute just as an advanced microphone. 167 00:23:54,030 --> 00:24:00,120 Okay, so this turns out to be a topological action. 168 00:24:01,350 --> 00:24:02,190 You have 169 00:24:03,270 --> 00:24:12,060 Efficient of motions all the certifications of motions for for the fourth years which appear or this equation of motions also lead to constraints. 170 00:24:12,750 --> 00:24:28,560 So you have so flatness constrained F is equal to zero, you have the towels container which appears in the user form, plus a term which is a bit unusual, but which is needed to take to to generate 171 00:24:31,410 --> 00:24:35,040 As a form HTTPS. So for me, if somebody 172 00:24:36,090 --> 00:24:38,100 Has a torsion on St. 173 00:24:39,390 --> 00:24:42,270 And if you have to, to curvature constraint which is a G. 174 00:24:49,950 --> 00:25:02,550 So this is a topological theory, it's not maybe key, but now you have actually directly in there is a field and the field. So, it is electric field and 175 00:25:03,600 --> 00:25:09,870 Pepper fields and what you can now easily put at least as silly. 176 00:25:11,880 --> 00:25:18,330 As a simplicity constraints which know just comes into forums that he has to be equal to start either he 177 00:25:20,250 --> 00:25:20,610 And 178 00:25:22,350 --> 00:25:31,890 I can find these papers which will save it here as a creation of motion for this form of action and the constraint on analysis of the continuum action. 179 00:25:36,390 --> 00:25:50,400 And you just mentioned that some observations. So the luggage might forgets to be fixed to be if it was a curvature was one curvature. So, this indicates us. It's also the case and BF series of simplicity constraints. 180 00:25:52,320 --> 00:25:56,940 Maybe second Johnson. Thank you, but also get secondary simplicity constraints. 181 00:25:58,230 --> 00:26:01,590 And geez to curvature consent evaluates to 182 00:26:03,090 --> 00:26:06,660 Some secular star f g 183 00:26:07,980 --> 00:26:12,330 So this if you translate to standard look on gravity variables. Actually, we 184 00:26:14,070 --> 00:26:20,640 Kind of look like San Antonio St. So it's actually the invasion of motion and policy formulation, as I mentioned, 185 00:26:21,750 --> 00:26:27,840 Until you see already here that this that G will be created to the 186 00:26:30,660 --> 00:26:35,250 Ancient times are expressed in the one in terms of one connection and the pilots. 187 00:26:36,690 --> 00:26:45,180 So G is a function of the one Connection. Connection you already see some constraints between the two connection and one connection. 188 00:26:46,980 --> 00:26:59,250 Okay, so, and puts it looks very promising. So you could also avoid people play around with this more and keep hold on, or one key automation. Was it 189 00:27:00,600 --> 00:27:01,110 Was 190 00:27:02,580 --> 00:27:04,950 Nothing available, which amounts to. 191 00:27:06,360 --> 00:27:15,930 To group for you transform. So you could ask, you know, what is the spin or the representation picture of this model and 192 00:27:17,040 --> 00:27:25,350 The connection between the for the spin Bobby model and a BSc G action or is a cool picture because it didn't exist yet. 193 00:27:27,300 --> 00:27:40,320 Most conjectured said it was given by model of quantum fleet quantum flat space, which we call it KBS also was defined by button, based on the call. 194 00:27:42,930 --> 00:27:45,240 So the rest of my talk. 195 00:27:46,560 --> 00:27:56,580 It's a plan to be to be presented with what's actually in our people. So it's a quantization or to be HCG action and the correspondence 196 00:27:58,290 --> 00:28:00,960 Will give it a bit postponements as a PDF motor 197 00:28:03,150 --> 00:28:17,370 As a key of offices correspondence that being not to construct a to group returns home. But actually, and solving odd also equations of motion or the constraints and 198 00:28:18,870 --> 00:28:23,040 He his idea was actually that this part of the constraints of foods, he 199 00:28:26,040 --> 00:28:28,860 Will be constructed. The only in that space of the ceiling. 200 00:28:30,270 --> 00:28:35,220 And you can say Otter also constraints and they have a consistent angel. 201 00:28:36,060 --> 00:28:51,120 And he defined support G network functions which you can send us a generalization of the sprint network function. So it's been a look functions in my house constraints and the G network functions environment has one of those constraints. 202 00:28:52,440 --> 00:28:57,510 And the two goals can send us a portion. And so one of those constraints. So usually those constraints. 203 00:29:00,450 --> 00:29:03,300 Okay, so are there any questions here. 204 00:29:08,010 --> 00:29:10,350 Okay, right, and I continue 205 00:29:13,170 --> 00:29:14,280 This a possible 206 00:29:16,560 --> 00:29:22,770 So, we have seen that action we can understand just also enforcing to constraints. 207 00:29:25,980 --> 00:29:30,600 So once that is complete and total constraint. 208 00:29:33,270 --> 00:29:40,830 And so that means it will sink. I can integrate out a good answer to connections. 209 00:29:41,910 --> 00:29:50,340 Either alive at the partition function nature just integrated was remaining feeds the connection and 210 00:29:51,420 --> 00:29:52,290 One forms. 211 00:29:53,730 --> 00:30:01,140 Lissa condition is the constraints and this. These are the data functions that the one coverage of anxious and 212 00:30:06,510 --> 00:30:12,300 Now you just need to pay again NATO allies. So extraction 213 00:30:14,670 --> 00:30:26,790 And so for the first one flightless we get to usually expansion. This is given by a portable global economies associated to the edges was an inside of it will face. 214 00:30:27,930 --> 00:30:33,420 So that's, that's the usual one flatness constraints and these will also 215 00:30:34,500 --> 00:30:36,180 Usually one anonymous 216 00:30:37,470 --> 00:30:41,910 Function contains actually. It's also quite straightforward contain 217 00:30:42,960 --> 00:30:45,630 It translates into the 218 00:30:48,090 --> 00:30:50,130 The associated vector 219 00:30:51,150 --> 00:30:52,110 To each edge. 220 00:30:53,880 --> 00:30:59,550 And so you get the X Factor and to extract all associated to the edges of the financial close 221 00:31:00,870 --> 00:31:03,540 So this gives us actually playing a total constraints. 222 00:31:05,040 --> 00:31:07,230 Now there's one subcommittee. 223 00:31:09,360 --> 00:31:22,530 Which I will explain going to see the torso two types of his family strangulation and this is know that they need to to worry about edge vectors which also see two edges. 224 00:31:24,870 --> 00:31:30,960 And which that you need to worry about in between you define these ethnic ethnic dogs. 225 00:31:32,070 --> 00:31:41,550 It's not a problem, an equity value of the victors associate to tiny let's hear you and I could you just choose one of the enabling technologies. 226 00:31:42,480 --> 00:31:52,620 Are some reference fame for for for the speed like to, and then you just have the consistency condition. And how's it be like door looks like a scene from the other free 227 00:31:53,910 --> 00:32:02,370 So here you have actors and separate all sharing it gives match. So you have to choose one or two step by eat all 228 00:32:03,990 --> 00:32:21,690 I said reference system for you actually go and, furthermore, you need to define how to call a transport you expect or who the other tip I, you know, which has this edge and this case if you're on CDs or two choices because you can always 229 00:32:23,250 --> 00:32:25,800 Cyclical cyclical on your edge. 230 00:32:28,260 --> 00:32:31,080 And so also the time at Oracle saying 231 00:32:32,760 --> 00:32:41,070 This not only involved the edge make those but also won Emmys, because these are needed to transport vehicles. 232 00:32:44,220 --> 00:32:45,810 And so in effect. 233 00:32:47,640 --> 00:32:54,960 If you think about know, doing, doing good for you transform if you just would do so for good for you transform 234 00:32:56,160 --> 00:33:06,810 So this it would do if you would have just be f series. So just one flatness constrains then you can do and so forth. We transform you would get the user 235 00:33:09,570 --> 00:33:11,700 It's a 10 or 15 Jason birds. 236 00:33:13,680 --> 00:33:16,290 But this piece we can't do that because actually is a 237 00:33:17,880 --> 00:33:20,190 One on one is also appeared in the portion 238 00:33:23,220 --> 00:33:30,720 And on the other hand, if you really wanted to, uh, to go for it and so on, they unfortunately as magicians do not know what it 239 00:33:33,510 --> 00:33:36,420 Is so there's no Peter YC available. 240 00:33:39,150 --> 00:33:47,430 What, what we did is actually to see that we can go forward by serving part of the data functions. 241 00:33:49,500 --> 00:33:56,250 And part and actually puts a little piece of time. You told us. In fact, we already 242 00:33:57,780 --> 00:34:00,420 Did a partial fleet as form in some sense. 243 00:34:01,680 --> 00:34:20,250 This part of it for you transform. We didn't do it as a states, some, but we did it by doing the integration my parts and the action so you can also start from from these constraints that connection to curvature is finishing. And then if we transform 244 00:34:21,420 --> 00:34:29,130 Our form and then if they actually finds a tiny closure as a contact form is a triangle closure constraints. 245 00:34:31,680 --> 00:34:37,620 So, so I think for the time enclosure constraints we would actually impose also took those constraints. 246 00:34:41,460 --> 00:34:58,440 And here he is again, the point is is partly transports appealing and the time constraints matter because this we have we have two choices pilot transports. And there are several choices on Channel two, one flight is concerns all these choices Uno momento. 247 00:35:00,180 --> 00:35:13,890 But the principles define us different versions of Pluto consent and a key inside is that being not even We not only have to take some time constraints, but we should actually add 248 00:35:15,270 --> 00:35:16,980 The edge simplicity constraints. 249 00:35:18,120 --> 00:35:27,750 And the actual physical constraints are basically what we had before impose it an edge backdoor pilot has floated around the edge itself. And it's stable. 250 00:35:28,770 --> 00:35:32,100 If you remember what I said on the previous slide. This ensures 251 00:35:33,210 --> 00:35:36,180 That the public transport which Troy see 252 00:35:40,500 --> 00:35:59,760 That's not met on a few things. And if you count. This gives you sleep conditions so that imposes extra exactly half of the one flight is constrained to the full flattens contango visit the whole only own G on the only on every edge would be vanishing 253 00:36:01,980 --> 00:36:02,580 Um, 254 00:36:04,590 --> 00:36:08,460 And it also has a continuum analogy. 255 00:36:10,230 --> 00:36:17,430 So was a time constraints come from the condition that the potion manages if you take again. 256 00:36:19,980 --> 00:36:35,310 To have certain condition you get f g is SEO and so that's actually the first can kayden at the edge simplicity constraints. I actually just a discrete those offices identity. 257 00:36:38,250 --> 00:36:43,740 So we will also imposes excellent the sequence things which you can understand as harmful to one. 258 00:36:45,630 --> 00:36:49,920 And at the end of it also make use of one gauge in my hands of the Pacific. 259 00:36:52,920 --> 00:36:53,370 Okay. 260 00:36:54,870 --> 00:36:58,470 So yeah, just to give a sketch sketch of support. 261 00:36:59,640 --> 00:37:01,170 Of the mechanism. 262 00:37:02,370 --> 00:37:04,410 We have obviously steps. 263 00:37:06,120 --> 00:37:07,620 Step one is 264 00:37:09,630 --> 00:37:15,780 This couple that important, the time constraints and the actual physical same 265 00:37:16,800 --> 00:37:21,840 As everybody basically a reduction and the degrees of freedom which certain salamis 266 00:37:22,920 --> 00:37:35,190 Effect. You can use these two constraints and you can prove that salamis a deuce to two cards and one part is completely determined by your adverts 267 00:37:36,090 --> 00:37:48,300 And if you go to time gauge it will be actually a rotation it as I thought only has one free parameter and this one free power meter mine was actually 268 00:37:49,620 --> 00:37:54,150 Curvature and if, again, if you go to have it set to be boost. 269 00:37:55,830 --> 00:37:59,460 Because it's an so for so for rotation. 270 00:38:01,110 --> 00:38:05,160 Which will be perpendicular to the to the time because the plane of Steiner 271 00:38:07,980 --> 00:38:08,250 Um, 272 00:38:10,470 --> 00:38:12,840 So yeah, it is. It all the G's. 273 00:38:14,130 --> 00:38:22,890 The free power meter left or if you discounters touchpads it just given my one. How many this English 274 00:38:25,440 --> 00:38:30,990 Now you can put this form of the GS back into the one flatness of St. 275 00:38:34,980 --> 00:38:57,330 It's an entrepreneur population and this case which we considered, which was a surface office complex it fixes modal one sign this expensive furniture cubbies eccentric curvature of a flatly embedded simplex. So you fix it and the curvature as a function of 276 00:38:58,410 --> 00:39:06,210 Subsets of your office complex and all what you need from the template. It's actually the length 277 00:39:07,380 --> 00:39:10,920 And so we just fix the seat us 278 00:39:11,940 --> 00:39:13,680 To be this explicit functions. 279 00:39:16,500 --> 00:39:20,910 Which are given by this isn't even an angle of reflection flattering. But it's complex. 280 00:39:22,470 --> 00:39:24,540 In terms of its edge edge links. 281 00:39:25,710 --> 00:39:28,140 So actually this year will be addressed left 282 00:39:30,270 --> 00:39:42,600 This to kind of enables excellent and CC to ingots so in this that the mid also use officer. So for each alliance or c x 283 00:39:46,590 --> 00:39:48,630 Last, so now we have 284 00:39:50,190 --> 00:40:00,330 This thing is, and what would you say you want for each one form for the data functions, which is the impulsive, meaning one flatness 285 00:40:01,890 --> 00:40:13,020 So we get what you what you need to remember here is that we get an amplitude patrols looks like exponential is so the variable also see to triangle. 286 00:40:14,760 --> 00:40:15,900 Sita is 287 00:40:17,280 --> 00:40:27,750 Valuable and you have asked us functions of capital city as he studied with angles of a flight simplex actual Piccoli 288 00:40:32,400 --> 00:40:36,630 So what you if you put that back into into the partition function. 289 00:40:38,730 --> 00:40:48,540 As this stone exponential is see Tom has a problem. He said concerts versus actual definition of suffering. 290 00:40:49,620 --> 00:40:59,190 And so if you're just left with these terms which I won't mention is times the healing is of a flat simplex 291 00:41:00,660 --> 00:41:01,620 And so this 292 00:41:02,670 --> 00:41:06,660 It to to get for each simplex and a new triangulation. 293 00:41:08,070 --> 00:41:12,180 So what you see here is basically the action. 294 00:41:13,440 --> 00:41:31,950 You have also this epsilon, epsilon is just giving you the orientation of the simplex as it follows home the fact that flatness constraint have two solutions one give us the hidden Inca if you would sit inside this template someone if using a heater ingots if you sit outside simplex 295 00:41:33,870 --> 00:41:34,500 S. 296 00:41:36,210 --> 00:41:39,210 O. 's that value because it comes home. 297 00:41:40,440 --> 00:41:43,470 So free transform what compared word Inger 298 00:41:45,090 --> 00:41:49,650 Living in this one the legs are continuous variables. 299 00:41:53,190 --> 00:41:54,390 And doesn't measure to 300 00:41:55,620 --> 00:42:03,900 Measure tome. Oh, you can determine Boyd demonic triangulation in this order and has been shown 301 00:42:04,920 --> 00:42:05,310 Lots of 302 00:42:06,450 --> 00:42:13,020 By our speech no longer need it be fights you and population in my own model. 303 00:42:15,150 --> 00:42:20,760 So yeah, you have to partition function and Ibiza basically the spin Bobby version. 304 00:42:21,810 --> 00:42:24,060 Of also be a CG 305 00:42:25,110 --> 00:42:26,670 based production function. 306 00:42:27,810 --> 00:42:30,570 I'm the sense that 307 00:42:31,740 --> 00:42:34,380 In fact, it turns out that 308 00:42:35,790 --> 00:42:36,270 The next 309 00:42:37,350 --> 00:42:48,690 Thing you labeled AND APPLAUSE And this all the time, the inequalities and post together. This is live, it's St. 310 00:42:49,830 --> 00:42:56,190 Can also be labels of representations and intertwine us also feeding tubes. 311 00:42:57,960 --> 00:43:14,940 And you can click on stop this action causes me to have this model believe directly from to walk representation silly as a sensor to simply simply totally arises from a collection of support to intertwine us 312 00:43:17,880 --> 00:43:25,740 So this is equivalent of office, beautiful picture of what we have seen in CD. 313 00:43:27,720 --> 00:43:31,140 Again here if you if you take the action to 314 00:43:32,220 --> 00:43:47,070 Hear you see more or less direct is a rejection, if you would really have the rejection st would not be a fee that either, but it would be to have a tiger or six expressed also function or two legs. 315 00:43:48,390 --> 00:43:57,510 So here's the point is, it s is a free valuable it's constrained on deck, because that's what you need to get to a data function. 316 00:43:58,560 --> 00:44:20,310 As a deficit ingots um and if you just start from this as a political action and so constrained. Again, this integration Magnolia as t minus at you, again, immediately see that solving for Michael O'Neill and solving for the constraints you get back to the match action. 317 00:44:28,200 --> 00:44:31,470 So this basically also proves that 318 00:44:33,540 --> 00:44:37,620 They can be F modesty related comes from the BSC G action. 319 00:44:39,120 --> 00:44:48,300 And it connects and also a picture and representation picture for this for beer for the BSC GT 320 00:44:49,950 --> 00:45:01,830 What we also provided in the paper is the differentiation of vulnerable space and the quantum geometry up operators which you can define on the spot here but space. 321 00:45:03,060 --> 00:45:11,040 So you basically is very much you have again with this ability to form one connection the connection. 322 00:45:12,570 --> 00:45:14,010 And the template many events. 323 00:45:15,330 --> 00:45:18,630 So these are represented by again beat 324 00:45:21,540 --> 00:45:24,120 Me that was associated to triangles. 325 00:45:25,800 --> 00:45:29,130 seasick boy leader relatives on so for 326 00:45:30,900 --> 00:45:31,110 Me. 327 00:45:32,430 --> 00:45:34,890 I couldn't get it to the whole mystique which are 328 00:45:36,180 --> 00:45:38,550 associated to the length of the bold letters. 329 00:45:39,630 --> 00:45:39,780 You 330 00:45:41,910 --> 00:45:42,120 Have 331 00:45:43,890 --> 00:45:55,440 Really been associated to the edges of the nation. So they present the edge towards and additionally you have many events which conforms to connection. So this will be to colonies. 332 00:45:57,120 --> 00:45:58,710 And they'll associate to the 333 00:46:00,180 --> 00:46:01,260 New faces. 334 00:46:03,420 --> 00:46:06,180 And to do it manually do it was a triangulation. 335 00:46:07,650 --> 00:46:10,770 And the timing. It's like the pine nuts. 336 00:46:12,060 --> 00:46:21,960 I do it through the lens and the edges on board to the faces. So you see that it always come on autologous eclectic selection. 337 00:46:26,130 --> 00:46:27,360 Be also provided 338 00:46:28,740 --> 00:46:33,750 A democratization and quantization of all the constraints. 339 00:46:35,100 --> 00:46:42,330 So in fact, in this topological theory that you don't even have any kind of factor ordering issues. 340 00:46:43,200 --> 00:46:54,540 And it's consistent in the sense that, though. This is like structure defined or the constraints constraints. I actually feel scans. So there's one flatness to flip this one goes into ghost good sense. 341 00:46:56,610 --> 00:47:09,540 And you can define a sub edge about constraints which is also first class in itself, which which is defined by one goes to goes into he implicitly constrained. So these are the constraints we have 342 00:47:10,410 --> 00:47:24,630 Imposed and capacity and this if you impose them. This leads to reduce the functions, all the functions which and only on the edge. Later on two legs labels and on the 343 00:47:25,860 --> 00:47:31,260 Healing is eco on just doing a power meter which you can define from 344 00:47:32,430 --> 00:47:33,120 Holland. Nice. 345 00:47:34,290 --> 00:47:41,490 So such functions would define what we call it g for Gauss network functions. 346 00:47:42,720 --> 00:47:48,900 And future. What will we be to delete these functions explicitly to like objects and 347 00:47:49,950 --> 00:47:54,390 Which come from to hope representations of his presentation matrices. 348 00:47:56,940 --> 00:47:57,810 And 349 00:47:59,340 --> 00:48:02,190 So the flatness constraints. So two flavors constraints. 350 00:48:04,140 --> 00:48:16,920 I would he explicitly. They have a very simple form. So the flavors constraints are defined for each said what you see so complex and 351 00:48:18,090 --> 00:48:23,730 The definition is similar to what we are us from the wall, one goes constrained 352 00:48:25,140 --> 00:48:35,100 And the demands that the connection many beds, which are suited to the two faces. If you some this connection believers. 353 00:48:37,560 --> 00:48:43,650 Associates associated to the faces which on a given. So this combination for Spanish 354 00:48:44,940 --> 00:48:50,850 So as a plus minus sign come from choices of orientation. So one has to set all 355 00:48:53,160 --> 00:49:05,880 The time again is one possibly has actually on a transport for these events or also one connection was a wonderful enemies appearances constraint. 356 00:49:07,140 --> 00:49:14,190 But given this right this constraint is the stress given also some over these events sigma 357 00:49:15,240 --> 00:49:19,890 It's easy to see. And I was going to give it to the templates, it's actually easy to see that these 358 00:49:21,390 --> 00:49:27,180 Two flavors constraint generator vertical translation for the template sector. 359 00:49:28,440 --> 00:49:43,650 So it says says this sentence Celsius. So it's a dual two vertices. And so give me two letters constraint would act on all the edges which are decent to given vertex and 360 00:49:45,330 --> 00:50:02,370 Since you have the same given each parameter in front of the goals constraint of this tool also to flatness constraint. This would lead to the just to adding a given vector to all the inspectors adjacent to this edge. 361 00:50:07,620 --> 00:50:18,000 Okay, so there has been also recent paper by by long for the living on safety and one of the points is also that the define 362 00:50:19,860 --> 00:50:20,100 That 363 00:50:21,120 --> 00:50:23,280 Include pirates actually 364 00:50:24,780 --> 00:50:34,650 I was very the tides are defined on boundaries and they have conjugated momentum from this point they can define the often constrained 365 00:50:35,370 --> 00:50:51,570 And so this is obligation because here we have also templates so to flatness constitute connection is quite a bit to the side. That's the two flatness constraints act as a center tune in and different office and constraints. 366 00:50:58,710 --> 00:51:02,850 Right. Let me summarize so 367 00:51:03,960 --> 00:51:04,920 This is more 368 00:51:08,550 --> 00:51:17,490 Advertisements at higher dt. It's an alternative approach to quantum geometry and look on gravity users. He itself. 369 00:51:18,570 --> 00:51:22,770 And US US poach to the quantum geometry. 370 00:51:26,430 --> 00:51:34,200 So here we generalize it to me. And I think has a particular advantages and sleep as one dimensions. 371 00:51:36,300 --> 00:51:45,420 So, we have seen that includes the templates and we get also geometric transplant Hamiltonian, a different model constraints and this type of sexual 372 00:51:47,880 --> 00:52:04,050 So what we put in particular did and our people is to construct the relation between the two group and representation picture of this quantum flat space model, and that includes a bona yes basis or constraints and the G network functions, the definition of the genetic functions. 373 00:52:08,220 --> 00:52:09,600 Rather, many things to do. 374 00:52:11,130 --> 00:52:14,610 On the on the mathematical side and on the precipice on it. 375 00:52:16,830 --> 00:52:29,220 This this project actually to look into to this model of quantum flat space time. It was actually motivated to understand calligraphy and slippers one dimensions. 376 00:52:30,060 --> 00:52:43,620 And it's easier to understand, philosophy and see first one dimensions, if you, if you go to quantum flat space. So here you can do that explicitly. I'm using both the picture and 377 00:52:44,940 --> 00:52:46,140 Put the presentation picture. 378 00:52:47,880 --> 00:53:02,640 Again, this is motivated by our broken and purpose one the enemy who local fee busy. The solution within this picture was essential to divide all these mice. Besides, we had 379 00:53:04,410 --> 00:53:14,760 So he can do you can think about similar setup to define two theories on and on the CD bonding. 380 00:53:17,310 --> 00:53:33,690 Here we use dramatic insight to construct basically to replace it totally transform, but we think that this actually can be used to define it to hopefully transform also for more general talks so that would be something on the mathematical side. 381 00:53:34,830 --> 00:53:35,610 Um, 382 00:53:36,630 --> 00:53:40,380 Another advantage is now we have be BSC G. 383 00:53:41,580 --> 00:53:43,590 As an action and 384 00:53:44,700 --> 00:54:00,840 It has been go by is and an openness, for instance, and coupling metal boy your defects to the St. Louis, and since f is a tool for what you need to couple 385 00:54:02,250 --> 00:54:03,030 Things. 386 00:54:05,280 --> 00:54:13,530 But now we have also the CG Terminator took a picture. So you can also come here, our tickets 387 00:54:15,600 --> 00:54:31,560 And in fact I'm highly engaged theory and higher categories are usually used to introduce boundaries of law and order I mentioned and your finger and so strings, basically, if you will. 388 00:54:33,450 --> 00:54:41,040 Because when I mentioned on here and articles, if you lower dimension one plus one dimension boundary. So that's 389 00:54:42,120 --> 00:54:44,310 All consistent with this idea of 390 00:54:46,320 --> 00:54:48,360 Now, being able to accomplish things in particular. 391 00:54:49,590 --> 00:54:59,220 But also relates to the caveat model because the PDF model was busy invented as a kind of the to copy Fineman items on offer. 392 00:55:00,330 --> 00:55:06,420 Particles propagating articles to some kind of lead quantum slide deck on 393 00:55:09,270 --> 00:55:16,920 Various, it could be also some connections with Telefonica key for the simple reason that they have a portion explicitly appearing in this window. 394 00:55:18,720 --> 00:55:28,980 For one interesting observation is to generalize too much of space time in particular to the place of war by, say something. 395 00:55:33,450 --> 00:55:35,610 Then, so this, this will be 396 00:55:37,830 --> 00:55:38,340 More 397 00:55:39,840 --> 00:55:41,100 Mathematical side. 398 00:55:46,650 --> 00:55:56,640 Of imposing simplicity concerns and face face into quantum so the fan voted interesting functions and this case I fled building blocks. We have teams at the SPS 399 00:55:57,510 --> 00:56:12,840 Commerce discrete spectrum because he's forgiven by these S3 buckets, which we have that valued as the length of this continuous vector was eventually these continuous spectral conforms affected be used for 400 00:56:14,340 --> 00:56:28,020 So if you if you're imposing constraints at NSF to be equal to the lens. You can also which which spectrum to actually survive in this case I'm most icing is actually to 401 00:56:29,430 --> 00:56:30,600 Look, it's a geometric 402 00:56:31,770 --> 00:56:34,200 Geometry, which is encoded in the screen opens 403 00:56:35,790 --> 00:56:46,380 To fly things could sense which generate nicely vertex translation and to use it to teach a better understanding and possibly to import them, it only sense 404 00:56:49,500 --> 00:56:52,020 Okay, so I would close here. 405 00:56:53,130 --> 00:57:01,920 I have only two extra slides. If anyone has a question about what the water to group and water to connection actually is. If not, 406 00:57:16,170 --> 00:57:17,280 We open for questions. 407 00:57:27,570 --> 00:57:28,260 If 408 00:57:30,750 --> 00:57:39,750 You see the definition of that is actually related to responding to form that appears in the definitional possible 409 00:57:42,000 --> 00:57:45,390 In the definition of what version of their 410 00:57:49,890 --> 00:57:57,510 Concert concert concert content is such as a relation to such as a look so 411 00:57:58,740 --> 00:58:09,150 Because it seems to me that it's to connection cheese. Who's exterior derivative was combined exterior is the 412 00:58:13,020 --> 00:58:13,980 Answer is not 413 00:58:18,120 --> 00:58:22,050 Okay, I would have to explicitly what's us wanting to form is 414 00:58:27,780 --> 00:58:28,680 I mentioned this. 415 00:58:29,910 --> 00:58:31,920 Possible relation to too. 416 00:58:33,060 --> 00:58:35,160 Long and yellow. 417 00:58:36,330 --> 00:58:42,240 And they define this quantity. In fact, in terms of cost of charges. 418 00:58:44,400 --> 00:58:51,570 Which come from integrations over regions or word boundaries of these features so 419 00:58:53,490 --> 00:58:56,790 And in fact, what what seems so 420 00:58:58,320 --> 00:59:08,280 I could be related to that. So the two flattens concerned, you can infect understand also kind of conversation conservation law. 421 00:59:10,320 --> 00:59:15,390 In fact, it's a it's a one bank identity, which then you can also understand that. 422 00:59:17,460 --> 00:59:18,300 And also to one. 423 00:59:20,640 --> 00:59:25,500 So you can you can understand also also 424 00:59:26,970 --> 00:59:28,680 As convert conversation. 425 00:59:30,570 --> 00:59:38,580 What an economist and us also equation of motion. If you import a Sophistic on St. This to connection. 426 00:59:39,630 --> 00:59:40,530 Seems to 427 00:59:41,760 --> 00:59:43,260 Claim is that it's finishing 428 00:59:45,570 --> 00:59:51,690 And if that's the case, it makes a dramatic interpretation somewhat difficult 429 00:59:53,580 --> 00:59:53,970 So, 430 00:59:55,080 --> 00:59:55,830 Its purpose. 431 01:00:01,110 --> 01:00:02,160 And the observation. 432 01:00:03,300 --> 01:00:06,480 On cello some physical constraint is related to the 433 01:00:07,680 --> 01:00:08,370 Matter. 434 01:00:09,510 --> 01:00:19,500 Is is cheap, is the script values to to flatness becomes one of the flux of his press ENTER depends for across the building. 435 01:00:24,630 --> 01:00:28,530 So I don't know what this platform in se, but it sounds awesome. 436 01:00:31,560 --> 01:00:32,040 Okay. 437 01:01:03,990 --> 01:01:04,380 Can you 438 01:01:06,480 --> 01:01:07,830 Know, see what's possible brackets. 439 01:01:07,860 --> 01:01:09,870 Between alanna Musa Fluxus 440 01:01:11,040 --> 01:01:11,430 And 441 01:01:12,060 --> 01:01:23,160 Needs background independence independent this meeting because two plus one. And yeah, you are this one plus two, can you can you explain was structural comes out and does a barbarian Mitzi parameter appear on the right hand 442 01:01:23,160 --> 01:01:33,270 Side so so to answer the last question we have not yet available in music parameter. But you think it's possible but 443 01:01:34,920 --> 01:01:35,880 I'm 444 01:01:37,290 --> 01:01:40,680 The beta quantization of these of these websites. 445 01:01:41,820 --> 01:01:44,430 So again, as you to select one 446 01:01:46,320 --> 01:01:56,490 Which is very similar to my which which is a b f which comes from to the afternoon. So this sector will look exactly like and look on 447 01:01:58,740 --> 01:02:03,840 So P is conjugated to G is a piece to commute and so on. 448 01:02:05,880 --> 01:02:12,120 Then only we have also put a subject exceptional on the Air Force ECHO and this is that 449 01:02:13,470 --> 01:02:17,220 10 megabits a canonical on you get it to the connection. 450 01:02:18,420 --> 01:02:25,740 And both are for. So, that makes sense. And the templates in this for so they actually mute. 451 01:02:27,240 --> 01:02:38,340 And just selecting like it's building the template feeds vanish. And so we still plan to the iPad with all these modern methods of driving subtracting 452 01:02:40,380 --> 01:02:45,900 Structures for silly only owners and so on. But that's just like instruction. 453 01:02:47,340 --> 01:02:58,650 And there you have said basically beefiest to be few there's two dimension to dimension things G sweet or one dimension, things that I asked me it over the edges. 454 01:02:59,670 --> 01:03:02,820 And so the conjugated valuable connection. 455 01:03:04,110 --> 01:03:06,630 Is defined on the faces. 456 01:03:07,770 --> 01:03:11,670 So awesome standard gravity. 457 01:03:12,780 --> 01:03:23,910 All these structures are basically consistent in the sense that the dimension it up those variables limits which are connected to each other, always defined on on 458 01:03:25,440 --> 01:03:32,220 An object like a link and the tool object. In this case, a triangle or an edge or face and so on. 459 01:03:32,970 --> 01:03:43,050 And so we could also buy down or constraints and even into discrete with all kinds of choices of public transport, you need to make 460 01:03:43,980 --> 01:03:56,520 And then you can compute that all these constraints effect on all to be first class. We have a consistent percentage, wha, and this constraint algebra and it reflects upon center support you. 461 01:03:58,260 --> 01:03:58,590 Thank you. 462 01:04:02,070 --> 01:04:04,200 Okay, any other questions. 463 01:04:04,770 --> 01:04:06,390 Yeah, it's how can you hear me. 464 01:04:06,960 --> 01:04:07,320 Yeah. 465 01:04:08,430 --> 01:04:12,420 I was when you spoke about the two representation labels that 466 01:04:12,570 --> 01:04:12,870 Was like 467 01:04:13,260 --> 01:04:13,560 Okay. 468 01:04:14,580 --> 01:04:23,040 And the fact that the SLA bows and integer clearly imposes some sort of constraints on the elves of that triangle. 469 01:04:24,210 --> 01:04:24,390 And 470 01:04:27,780 --> 01:04:28,680 Oh you disappeared. 471 01:04:29,580 --> 01:04:37,290 Oh, no. I was just wondering if the the constraints imposed on the elves have some interpretation in terms of the representation theory. 472 01:04:38,850 --> 01:04:42,840 By Tuesday yesterday was being imposed on St. John's day 473 01:04:43,890 --> 01:04:48,570 Well, because there's only some else that will satisfy that the the area. 474 01:04:49,230 --> 01:04:51,690 Was every else. Yeah, so 475 01:04:52,890 --> 01:04:55,440 If you import kind of simplicity 476 01:04:56,820 --> 01:04:59,070 That's what you're asking. Yes. 477 01:05:00,150 --> 01:05:01,140 Yeah, in fact, 478 01:05:07,350 --> 01:05:10,290 If you, if you do it. And this, let me see in a fee. 479 01:05:12,840 --> 01:05:14,940 Which I'm seeing naive because 480 01:05:16,500 --> 01:05:18,780 There will be also secondary constraints you 481 01:05:21,330 --> 01:05:21,720 A picture. 482 01:05:21,810 --> 01:05:34,920 Which I have not looking. And actually, if you, if you look at this, if your answer is contained in the actual meal. You see that lunch, right. You play against actually fixed to be to be the deficit in so 483 01:05:36,510 --> 01:05:45,780 Which means you can expect that this constraint. The second house, but also is always the case with this client. So now you can choose 484 01:05:50,040 --> 01:05:53,520 It's sort of a textbook style you actually that you have to go back to classic a silly. 485 01:05:55,560 --> 01:05:57,720 And go to the advocates and so on. 486 01:05:58,950 --> 01:06:00,930 It can also choose any kind of 487 01:06:02,280 --> 01:06:04,530 Version, which is just a spectacle quantization. 488 01:06:05,610 --> 01:06:08,280 And what I want to say is it's not very clear. 489 01:06:09,540 --> 01:06:20,100 If you will really go back to formulate formalism that opposing this constraints that the SEC between and one is this 490 01:06:21,240 --> 01:06:32,820 Very good insight that you should. That is actually survives assume this is what survives and effect. It's an element, which has been made by Voinovich just that he claims. 491 01:06:33,300 --> 01:06:44,940 Or Zelda slick that solutions on the air is one of the solutions is at all edits, or just equal to one, for instance, or equal to some global scale. 492 01:06:48,000 --> 01:06:50,370 Which I don't think it's a nice solution. 493 01:06:51,420 --> 01:06:56,550 Because I usually if you go back, if you go to larger, larger 494 01:06:59,430 --> 01:07:01,650 Next variables that you will find 495 01:07:03,540 --> 01:07:04,650 More solutions so that 496 01:07:05,670 --> 01:07:20,010 So the question is, is it likely to do if you do it, then you will find stone, stone constraints on on the it's it's maybe an interesting question. How these constraints behave 497 01:07:21,090 --> 01:07:23,130 If you go to larger links for me. 498 01:07:24,840 --> 01:07:28,650 And all this events to find a dense set of solutions or not. 499 01:07:30,780 --> 01:07:31,500 Yeah. 500 01:07:33,630 --> 01:07:34,320 Good. I 501 01:07:35,910 --> 01:07:38,010 Like it just comes creation. He 502 01:07:39,720 --> 01:07:40,020 Said, 503 01:07:40,320 --> 01:07:44,640 Before we have. So to see order as one 504 01:07:44,670 --> 01:07:45,210 Yeah. 505 01:07:45,690 --> 01:07:46,470 And then 506 01:07:48,780 --> 01:07:49,650 Which is the contract. 507 01:07:54,840 --> 01:07:56,700 Yeah, that'd be continuous partially 508 01:07:58,560 --> 01:07:59,250 Series. 509 01:08:00,840 --> 01:08:01,560 Continues 510 01:08:03,600 --> 01:08:03,840 So, 511 01:08:03,870 --> 01:08:12,000 So partially or two. So to see or the scope and you would expect that some of these SS 512 01:08:13,320 --> 01:08:25,680 Have to be continuous another interesting question. Just go to curve building blocks. If you go to craft a TD and maybe the editor become the seat, but it's when somebody to me. 513 01:08:27,330 --> 01:08:35,850 So certainly there's an interesting question register which kind of spectrum might survive if you try to also success equals. Thanks. 514 01:08:40,770 --> 01:08:41,310 Thank you. 515 01:08:41,550 --> 01:08:43,020 Are there further questions. 516 01:08:50,160 --> 01:08:53,490 Does not appear to be the case. So that's Bianca again. 517 01:09:00,150 --> 01:09:00,690 Thank you all. 518 01:09:01,470 --> 01:09:01,740 Right.