Jorge Pullin: Okay, so today we have a panel on corner degrees of freedom and so that's your however fee will be chaired by low fidelity and the speakers are Mike giler walk on villain and Daniel different city orange.
Jorge Pullin: Okay.
Laurent Freidel: Hello everyone and.
Laurent Freidel: Thank the organizers for inviting us to speak on the.
Laurent Freidel: subject, which is the you know corner degrees of freedom and service geography, I change my way to corner and you'll understand why so we're going to hear from mark for gang and then nearly and the idea is that.
Laurent Freidel: You know the talks will go from small to big from the corners muttering kinematics that might be described and again we'll talk about causal diamonds and dynamics and then he will talk about a synthetic infinity.
Laurent Freidel: The purpose of this framework or this new perspective is really to address several fundamental issues that are present in the context of spin form and look at.
Laurent Freidel: The first one is that the framework would propose is a framework where quantum geometry carries a presentation of the imagery group and the Lawrence imagery group which is compatible with subsystem decomposition.
Laurent Freidel: And it's also a framework where phenomenal results, such as the owner, the music parameter.
Laurent Freidel: And the quantization of the area can be understood directly in the continuum in the usual language of effectively theory resolving without having to resort to a loop presentation.
Laurent Freidel: This is a framework where non parametric column gravity results that were used to spend forms connect seamlessly to the asthmatics approach of quantum gravity.
Laurent Freidel: And, and the key idea, there is to focus on the symmetry and to go from corner symmetry to s&t symmetry and reveal the sinister holography picture.
Laurent Freidel: In the stoke each speakers as proximity 15 minutes, I asked you to ask questions at the end of the talk only.
Laurent Freidel: Which are clarifications questions and then what we would have is that, after the three speakers will have longer discussions on the on the sets of results, so please postpone your more conceptual and bigger questions to the end, thank you.
Laurent Freidel: mark is the first.
Marc Geiller: Alright me share my screen yes.
Marc Geiller: Okay, so thanks again to the organizers for inviting us, and thanks for introducing this panel it's my pleasure to speak with.
Marc Geiller: These four colleagues here and to speak to your so i'm giving some kind of motivations here, and the first motivation, of course, is to motivate why we're interested in the study of boundaries.
Marc Geiller: So the reason for this is that, as you may know, important physics happens at boundaries.
Marc Geiller: And what we mean by this is that it's fairly generic in any theory in even for that matter, not necessarily against theory, even for comments matters systems quantum mechanical systems.
Marc Geiller: You have the appearance of something that people call edge or surface boundary or corner, I want to be a bit agnostic about the terminology here, and you have the appearance at these boundaries of modes or charges or states or However, sometimes people call it.
Marc Geiller: The point for us what's more to be more precise, is that engage theories, so, in particular for our purposes in the case of gravity.
Marc Geiller: boundaries may support some extra structure which you won't see if you don't have a boundary and this extra structure is typically the appearance of charges and symmetry address.
Marc Geiller: So just to state this once and for all, we have to keep in mind that boundaries may be fairly general, for example, the boundary may be.
Marc Geiller: At infinity for examples cry plus in unison politically flat space time the boundary may also be the horizon of a black hole which is just sitting on your left or your right.
Marc Geiller: So a finite distance and also interestingly, the boundary can also be in a sense of fake financial boundary if you're interested in computations such as entanglement entropy, for example.
Marc Geiller: Now I want to say why studying this is actually not really kind of betraying our origins and where we come from, but it's just in line with what we.
Marc Geiller: What we're all interested in here because it fits the logic of Luke quantum gravity.
Marc Geiller: Why does it to the logic of energy well, because this is just pushing further the idea that we have to take seriously the structure which is given to us by classical general relativity.
Marc Geiller: So here we mean the fine structure given and unravel by studying what happens with boundaries in general volatility.
Marc Geiller: And after all look on gravity was proposed and beautifully constructed as a quantization of general relativity.
Marc Geiller: which puts precisely the classical symmetries of the theory at the Center of the game.
Marc Geiller: And we know that usually what what we have constructed is a certain of representation of the form of isms and also importantly, as you to symmetry, so why not push this logic further if we discover new symmetries and also, in a sense.
Marc Geiller: Some approaches some versions of quantum gravity, you can think of them as being in a sensor bottom up, where we build the space time.
Marc Geiller: As in a sense of gluing and of course greening of small microscopic building blocks, so we start with some local data and build the big from the small.
Marc Geiller: So, because of this, we have to wonder whether this prescription is actually compatible with similar statements, if they are made at the level of classical generativity or classical gauge theory, so what is the notion of a local subsystem in theory.
Marc Geiller: Also, I think that this gives the important new opportunities for quantum gravity because.
Marc Geiller: I think it's important to try to maybe reconcile some aspects of energy which may be from the outside perspective can be seen as being too.
Marc Geiller: belek based and kind of forgetting or ignoring the issue of boundaries reconciling this with quote unquote holographic approaches or in the very broad sense.
Marc Geiller: in the sense that approaches which are.
Marc Geiller: Based already describing and taking into account physics and structures which happened at the boundary so maybe we have the opportunity of reconciling these two pictures.
Marc Geiller: Also, this is exciting, because it gives maybe a possible test for.
Marc Geiller: Having new viewpoint on the classical underpinnings of quantum gravity.
Marc Geiller: And, in particular, I think the four of us would argue that there is a possibility for really understanding the classical level, the wall of the emergency parameter.
Marc Geiller: and also the fact that we work with our drivers so maybe we have even on the kind of the ultimate goal would be as, then you, they will say that maybe we even have the possibility of testing this with observation of some maybe do a synthetic charges.
Marc Geiller: And also it's interesting because well already, we have to give credit to the work that has already been done.
Marc Geiller: I think it's an opportunity for us to go and solve problems which are laying around in other communities.
Marc Geiller: Because look at him gravity tools are in a sense, well suited for the quantization of boundary symmetries.
Marc Geiller: And there is the work of many people and sorry if I forget some.
Marc Geiller: which have already proposed many tools to deal with you know some structures which you might want to use to describe notions of photography and boundaries.
Marc Geiller: sensor networks boundary states boundary duels of 3D Luke quantum gravity there is all this material which is there, and which I think it's Nice that we have this at our disposal.
Marc Geiller: OK, so now, I want to make the sponsor bit more precise and first just that we agreed to kind of tell you and summarize what classical general relativity tells us.
Marc Geiller: So what we learned from the classical theory, something that has to do with the notion of charges and symmetries.
Marc Geiller: When engage theory, we have beautiful theories biota and more precisely to theorems and if we combine these two theorems they tell us that to symmetry transformations we can assign.
Marc Geiller: Co dimension to objects which, generally speaking, we record charges.
Marc Geiller: And the general structure of these charges is as follows, so as you see, on this equation your attendees charge by contacting the cemetery confirmation that XI like a different, more freedom.
Marc Geiller: With the syntactic structure, generally speaking, you see, because of this data slash notation discharge might not be.
Marc Geiller: interchangeable might not be a total evaluation on face face, but the general expression that discharge will take is a piece, which you can call a true.
Marc Geiller: newtonian beast which is interoperable and maybe some flux beats this flux piece, as you will see, also from the talk of all gang and daniella.
Marc Geiller: is understood now for several years since based on what this work on kind of symmetry properties of gauge theories engineer on a DVD that is flux is related to the presence of possible, for example, of ideation in your face space so degrees of freedom, leaving.
Marc Geiller: Your region and the fact that you are genetically dealing with open hamiltonian systems, so this is not just the kinematic and information which is encoded in these charges, but also a very important dynamic on information.
Marc Geiller: Now, if you ask how such a charge is evolving well you act again with another confirmation on one of these charges.
Marc Geiller: And again here, you can loosely speaking see that the person bracket of discharges is, in the sense or term which kind of stays within some sort of symmetry algebra quotation, and also a DC patty term, which is a flux, due to the term sorry, which is the term due to the FLEX.
Marc Geiller: So now why I want to hear made this distinction between rotation anticipation, is to kind of stress that there is a kind of separation between the notion of kinematic will.
Marc Geiller: charge and kinematics symmetry and then and dynamic and ocean more precisely what happens fairly generically is that discharges when you compute the algebra.
Marc Geiller: They form a symmetry group which we could call the corner symmetry group which you see on this little space time.
Marc Geiller: diamond here four dimensional where the hyper surface Sigma and the code I mentioned to boundary of this.
Marc Geiller: hyper surface is called so that's the corner and you can assign a symmetry group to this corner, which genetically has the structure, so there is a cinematical.
Marc Geiller: subgroup which, as you see, in green is the subgroup in a sense, you can think of it as preserving the boundary of this hyper surface, so you can think of this as being cinematical.
Marc Geiller: And then there is a dynamic apart the dynamical part is in a sense, composed of transformations which moving the radial direction and which moving the temple direction, so the probe the other degrees of freedom which lie outside of your slice.
Marc Geiller: that's kind of the general structure of this cemetery group now what's interesting for our purposes is that.
Marc Geiller: One can show.
Marc Geiller: You can actually show, for example in classical general volatility that most of this information here actually certainly depends on the formulation of gravity which you choose.
Marc Geiller: More precisely, for a given formulation of gravity let's call it F, for example, the ticket formulation.
Marc Geiller: Well, you can show that the syntactic structure of the theory which controls, essentially the charges and the algebra and what this dynamic and information.
Marc Geiller: related to the flux well the syntactic structure of the theory, the formulation F, you can always manage to write it as universal a bulk piece, which is nothing but the ATM syntactic structure.
Marc Geiller: Plus, you see here i'm writing a boundary term D of something which you can think of as a boundary syntactic structure and this boundary syntactic structure is a formulation dependent quantity.
Marc Geiller: Now, one of the episodes of this of the statements, is that, in particular, you seen the boundary in the corner of symmetry group which I wrote above in the kinematics part there is a subgroup page, which I have not specified.
Marc Geiller: And, in particular, there is a sense in which the subgroup age is actually sensitive to the formulation which you choose.
Marc Geiller: So just to give some examples here administering some examples of formulations of gravity which you may study, so the ADM formulation.
Marc Geiller: Or the action hilbert formulation which we should remember just differ by a boundary term but, even if that like engines differ by a boundary term.
Marc Geiller: The syntactic structure differs by a boundary syntactic structure and because of this, the charges are not the same, and also the corner symmetry group is not the same.
Marc Geiller: You see that there is an extra normal SL to our subgroup which is present in the Einstein hilbert formulation and which is not there in the idiom formulation.
Marc Geiller: So the fact that at the classical level, you can exhibit different symmetry groups means that if now you propose a quantization scheme based on promoting the symmetry group.
Marc Geiller: The quantum theory, for example, by working with the presentations of these groups.
Marc Geiller: These gives the possibility of having in equivalent quantization because the classical symmetry starting point is actually different in different formulations.
Marc Geiller: So for our purposes, of course, what is important is to ask what happens if you work with variables, so instead of the Ashton hilbert action.
Marc Geiller: We work with the Einstein katha action or if we add the topological Horst term, so the Einstein capital host action.
Marc Geiller: And as you see here, as I will argue on the next slide This gives rise to sort of tangential SL to our symmetry.
Marc Geiller: and also to Intel boost confirmations or to the horror internal organs work if you work with Damien Z parameter so now, can we just derive immediately a lesson from this classical observation about general relativity well some implications.
Marc Geiller: The implication, which is interesting for for us is that we can derive from this an argument, saying that the areas that I have to be discreet.
Marc Geiller: and build this argument just from the classical theory and at the continuum level.
Marc Geiller: So to do this, let me make explicit now what I wrote on the previous slide, namely writes the syntactic structure which we use in Luke quantum gravity so that's the syntactic structure.
Marc Geiller: Coming from the classical Horn section, so the action in connection and Ted had variables, with the emergency parameter, which is hearing green.
Marc Geiller: And right as we wanted the syntactic structure as the ATM syntactic structure in the bank and then a boundary syntactic structure which you see here, I put different colors so capital, he is the usual.
Marc Geiller: continuum analog of the quantum gravity FLEX N, is the internal normal that is a kind of an internal version of the normal of the DNA formulation.
Marc Geiller: it's also normal, which plays a very important role in spin forms so it's Nice that and, of course, it was known that this quantity is already present in the classical theory.
Marc Geiller: And you see that the emirati parameter introduces this extra boundary syntactic structure which depends on the frame in which is here in Brown.
Marc Geiller: So now, this flexes and I think they just found the familiar Su to algebra of energy flux algebra.
Marc Geiller: And now what's interesting is that, from the structure we can derive the fact that the tangential metric which is constructed from this tangential frames.
Marc Geiller: At the code I mentioned to corner s forms actually an asset to our algebra and you see that this SL to our algebra has actually.
Marc Geiller: When he's actually controlled by the image, the parameter, so this is telling you classically that you see that if you send the Multi parameter to zero.
Marc Geiller: Well, it would seem that the metric on the boundary is actually commuting with itself, but that's not the case, if you have the emergency parameter now what's very interesting is that if you compute the Academy of this as to to symmetry.
Marc Geiller: Then you will find that the customer is related to the St booker's India, and also to the square of the area elements with an important minus sign now this minus sign is telling you that if you were to.
Marc Geiller: represent this in the quantum theory, you would be forced to work with the discrete series of presentations of a cell to our because this kazmir is negative.
Marc Geiller: So this is the results kind of indicating that from the continuum classical level.
Marc Geiller: If you take the point of view that you start with quantum gravity the symmetry content that you extract from the boundary.
Marc Geiller: tells you that you have a quantization of the area elements so here, I wrote an area elements are elements can be some measures comes in, to set either a continuous form or a discrete one This tells you that you have to work with some kind of optimistic discrete is never.
Marc Geiller: Now, another lesson which is a bit more broad but which will allow me to transition was the talk of our gang and Daniela.
Marc Geiller: Is that when the symmetry structure, which I mentioned on the previous slide.
Marc Geiller: More generally speaking, you can think of the symmetry is actually controlling the behavior of subsystems so I wrote this little drawing here to show a finite sub region.
Marc Geiller: Of a spatial manifold Sigma with the compliment Sigma bar and i'm drawing here the familiar fact that engaged theories physical observable or extended non local objects here in blue is a Wilson line.
Marc Geiller: So if you have such an agent violent observable and then you want to work or describe a sub region.
Marc Geiller: Well, you have to potentially worry and take into account the fact that the sub region may actually intersect and cut in half, these Wilson lines.
Marc Geiller: Because of this, you have to keep track of the endpoints which anchor the Wilson lines on the boundary and that this anchoring points you have a non trivial action of some symmetry group which is nothing but the corner of symmetry group which we talked about so far.
Marc Geiller: So you can think in the sense that.
Marc Geiller: yeah so the symmetry is they actually tell you how you should actually glue together or cut subsistence.
Marc Geiller: And the subsystems can actually be two things they can be just a finite sub region, then you want to ask how to get the sub regions and hope to glue them back together.
Marc Geiller: And, in a sense, it can also be the whole of space time if you adopt this again loosely speaking holographic point of view, in which you want to ask.
Marc Geiller: From the knowledge of some boundary information, how much kinetic constructs about the bug and then you, they will, I think, mentioned this a lot.
Marc Geiller: So just the last point, which is bit more broad is to say that, from this, I think we should conclude that the logic of look quantum gravity if pushed further.
Marc Geiller: tells us that we should actually aim at labeling the states we work with we reduce the burden of presentations of the boundary symmetry group or suitable boundary symmetry group.
Marc Geiller: which happens, which is unraveled when we studied this boundary structure of general relativity so maybe we have to kind of propose some extension of.
Marc Geiller: The networks are the data that we're working with, and there are already some proposals for this, which Wolfgang and then you, they will now review, so I give the floor to Oregon now.
Laurent Freidel: Thank you, maybe before the floor, I think, is the.
Laurent Freidel: Malaysians for clarification clarification questions if any.
Laurent Freidel: Okay, I don't.
Laurent Freidel: see any in that case.
Marc Geiller: Okay, then I pass it on to Wolfgang and then.
Laurent Freidel: Again, then.
Laurent Freidel: it's perfectly on time.
Laurent Freidel: hear you.
Wolfgang Wieland: Oh sorry.
Can you hear me.
Laurent Freidel: Yes, yes.
Laurent Freidel: Wait a second.
Laurent Freidel: Can you stop.
Wolfgang Wieland: Yes, sorry I mean.
apologies.
Okay.
Wolfgang Wieland: Well, first of all I would like to thank the organizers for the.
Wolfgang Wieland: For the opportunity to speak here, and I also would like to thank my colleagues, which, for the very nice discussions we had in preparation of this event.
Wolfgang Wieland: When considering a game theory certain conflict arises, a conflict in our understanding of the theory, so what happens is that they are, if we look at the theory in a finite region.
Wolfgang Wieland: There are physical degrees of freedom inside and then they're engaged symmetries but what happens, by introducing.
Wolfgang Wieland: boundary a corner, is what happens is that otherwise i'm physically engaged directions turn into physical boundary degrees of freedom and I call this a conflict, not to be provocative, but in reference to a.
Wolfgang Wieland: Important aesthetic aesthetic problem in architecture corner, what happens when introducing a quarter is that symmetries are broken and this creates a conflict, the conflict in our understanding and this conflict is an is the origin of many exciting developments in our field.
Wolfgang Wieland: mark has already mentioned some of them, I will go on and.
Wolfgang Wieland: Further into some of the developments that have been achieved in the past couple of years.
Wolfgang Wieland: but also some of the developments I won't mention, for instance, the relation to quantum reference frames and also I won't speak about.
Wolfgang Wieland: Black credential be and gluing and cross training and.
Wolfgang Wieland: topic so conversations frames, this is a topic of very great interest in Vienna at the Institute for quantum optics and column information.
Wolfgang Wieland: And gluing and post meaning goes way beyond the three of us endorser is an important part of many other developments in our field from young lady, please, to.
Wolfgang Wieland: economically.
Wolfgang Wieland: From general relativity so now let's go on to study the problem at a simplified level, so instead of looking at the.
Wolfgang Wieland: Full nonlinear face space let's try to lesson so let's try to learn some lessons from linear rise gravity.
Wolfgang Wieland: The idea behind this is to know the dimension of a manifold it is way enough to know the dimension of expansion space and the dimension.
Wolfgang Wieland: Of the physical hilbert space is the dimension of comments or tells us how many observers, they are to begin with, so let's consider this eclectic structure we saw in the last talk, so the one for urbanski.
Wolfgang Wieland: General relativity and first order variables with additional with an additional corner that contains variations of the normal so we start out with flat solution of the feet equations the Tetra is just a differential have some international coordinates and there is also some.
Wolfgang Wieland: Arbitrary case transformation that allows us to take the screen into any other cage equivalent configuration and then we look at perturbations linear perturbations around the flat solution.
Wolfgang Wieland: And likewise for the connection it is a flat reference connection, plus a different stance or delta, which is just a gradient of the perturbation essentially.
Wolfgang Wieland: And now we want to evaluate the simplistic structure around perturbations of flat.
Wolfgang Wieland: Space and what we get is this what we get is that in the future of space time there are radiative modes, which are.
Wolfgang Wieland: captured by the variation of the perturbation the university equation, but on top of that, there are boundary terms and what is crucial to understand for this.
Wolfgang Wieland: For this whole business is the fluctuations of the embedding functions because of coordinating bonds because of general covariance only show up at the boundary of space time and if we.
Wolfgang Wieland: now take this expression, all the way to space like infinity what we find is that what we recover are the usual edm charges imposing the usual for have an parity condition conditions in terms of the electric and magnetic components of the white answer.
Wolfgang Wieland: Now going further, now we have in the last slide the last last the previous slide maybe a bit misleading because it tells us that.
Wolfgang Wieland: It seems to tell us that Detroit office charges charges trivially integral, but this is only so because we neglect because we put the TV at the linear is leverage if we go to the full non automotive theory, there will be also have to take into account surfing direction.
Wolfgang Wieland: And in our words radiation and flux and then it happens separately, I know canonical generators anymore for timeline or radial diffuse that would enlarge the system or move it forward in time.
Wolfgang Wieland: In fact, to characterize gravitational and subsystems or subsystems engage theories several choices, need to be made so and I like to repeat this.
Wolfgang Wieland: So i've spoken about this before and I want to make this point clear, because it is an important point.
Wolfgang Wieland: So we have to characterize initial data on the so corner data at two dimensional cross section, these are charges, but on top of that, we have to characterize the flux flux that leaves out the system.
Wolfgang Wieland: Furthermore, we also have to make a choice for how to extend the corner into a virtue into space time how the corner itself evolves forward into space time to understand that it is a dynamic system.
Wolfgang Wieland: And then the following, I will go to regions of space time that are.
Wolfgang Wieland: bounded by non hyper surfaces going to another hyper surface going to not boundaries is advantageous because there's just more structure available.
Wolfgang Wieland: With respect to which we can characterize radiation, furthermore, it is a system where radiation can only go out or 14.
Wolfgang Wieland: Furthermore, they are some ingenious new developments that are in to understanding the coma charges on the cabal Ian face space.
Wolfgang Wieland: For more geometrical perspective, introducing a field space connection, so this is very intriguing I find this very intriguing, but there are some issues that.
Wolfgang Wieland: I think needs to be clarified, especially how to understand, changing the system size now let's jumping right into this course or diamond prescription.
Wolfgang Wieland: We are doing Dupont gravity, so we want to understand the effect the messy power meter and the sweetness of space has on radiation, for example on observer of on observing radiation so that's why the.
Wolfgang Wieland: Our starting point is the horse action he written in terms of speed no barriers ourselves to our variables efforts, the curvature seeing maybe is the self who are part of their area to form, Eva g.
Wolfgang Wieland: And, depending on the boundary conditions chosen different boundary boundary terms or different boundary few theories will emerge in here we restrict ourselves to.
Wolfgang Wieland: This directly time boundary conditions where he equivalents class of the intrinsic geometry of the not hyper surface class a you want connection and a billion connection on the novel hyper surface he speaks and.
Wolfgang Wieland: Accounting then reveals that disclosure criminal class characterizes is characterized by two degrees of freedom, the two degrees of freedom of the radiation passing through the.
Wolfgang Wieland: Non hyper surface and then the next step is to look at the face face to associate a face face to the partial cushy hyper surface.
Wolfgang Wieland: anchored at high risk to get as nicely explained by mouth in previous talk together bark piece, but now, Sir, a corner piece, and now we can ask us more primitive pressuring stealth quantization before.
Wolfgang Wieland: pages face face of this theory let's consider only the corner degrees of freedom and asked whether can better we can have a representation of economically combination relations of those corner charges which satisfy a Heisenberg algebra derived from this syntactic structure.
Wolfgang Wieland: Now, out of these Heisenberg charges, we can construct two sets of harmonic oscillators by contacting them via user Fuck quantization so choosing a fork back home.
Wolfgang Wieland: We obtain we can construct physical states, states that satisfy the reality conditions, the constraints that we need to impose.
Wolfgang Wieland: And on the solution space of these constraints what we find is that the area of flux, that is to say that oriented area of the two dimensional cross section of the non hyper surface has a discrete spectrum.
Wolfgang Wieland: And what is very nice but of this argument is that it's purely that it does not rely on.
Wolfgang Wieland: On on a specific representation, so I have developed it using a fox representation, but you could equally well work with a standard.
Wolfgang Wieland: spin that direct representation, where you would have punctures hitting this this.
Wolfgang Wieland: Crop two dimensional cross sections and then, just like in the previous talk, you would get a real expectations at these punctures but what I want to stress is that the sweetness of area is more general than that it does not rely.
Wolfgang Wieland: On the usage of tubes or discrete speed networks any sensible conversation of these algebra will exhibit such a descriptors.
Wolfgang Wieland: But now we have what we have in text or what we will both be having fact is a hierarchy of face faces in quantum theory is will be a hierarchy of human spaces, there is not only.
Wolfgang Wieland: them there is not only a face space for the animals or the boundary most at a two dimensional perception, they also, we also need to characterize the release the free initial data on the non hyper service itself.
Wolfgang Wieland: And now the non hyper surface comes in handy it's geometry, because it has more structure and we can, which allows us then to.
Wolfgang Wieland: Permit rice, the geometry as follows the induced metric and then our hyper surface is the general this is your class class metric.
Wolfgang Wieland: Is similar direction being the direction of the knowledge and or interest itself and, just like in four dimensions, we have tetris in three dimensions, we have.
Wolfgang Wieland: trials, since he the geometry is essentially two dimensional we can introduce diet diabetic one forms intrinsic to the novel hyper surface and the any such.
Wolfgang Wieland: One form can be paradise by with in terms of a fiduciary one form that is transfers to this non directions times a consumer thought store that gives the overall shape times and so too are shaped transformation and these two are shaped transformation is pretty much the gem that.
Wolfgang Wieland: The buyer and a lot of the corner so to our data that mark kyla spoke about in the previous talk.
Wolfgang Wieland: To fully complete the face face description, we also need a choice of time this one comes handy to solve the Machado equation, which is one of the constraints of in this moment feminism.
Wolfgang Wieland: If you then take the whole section, so the starting point of the old LPG program and.
Wolfgang Wieland: Take the simplex its structure for the boundary conditions chosen and evaluated on the non hyper surface what we get is this kinematic face face.
Wolfgang Wieland: That consists of a term that encodes the shape degrees of freedom on the normal hyper surface class additional a billion pop.
Wolfgang Wieland: they're clearly a billion part encodes the expansion, the time function deluxe function, and it also includes food most crucially for understanding of the sweetness of area.
Wolfgang Wieland: Also, their their comfort factor which is now canonical the conjugate to you want connection again we see area.
Wolfgang Wieland: And we have flux is economically contribute to an angel, hence the sweetness of area and once again this term comes with a multi parameter that governs the strength of this term indirection.
Wolfgang Wieland: Now to on the physical hilbert space, not all these degrees of freedom are independent, we have to impose constraints.
Wolfgang Wieland: first and second class constraints, the second class constraints, give the person brackets for the free radiative data on the generic not hyper surface.
Wolfgang Wieland: In terms of these complicated looking expression so highly nonlinear but the point being if we take no limit to infinity then this asset to our.
Wolfgang Wieland: picks up server has has some terms that for us in different orders as one upon our different one upon our expansion and.
Wolfgang Wieland: In the limit to infinity only the leading order survives and we get what we get is just the right, the second line goes away and we just left with the computation relations.
Wolfgang Wieland: That we find on the redemptive face face or of future non infinity, for instance, in addition to that, in addition to the second class constraints they also first class constraints that imposed against symmetries, namely you want transformations and if you move along the normal race.
Wolfgang Wieland: Finally, let me summarize in my talk I focused on the results that i've achieved thus far, so I have been looking at.
Wolfgang Wieland: boundary conditions for radiative data and characterize how this is all this is affected by the interaction of the Bailey municipalities that what we find is.
Wolfgang Wieland: That the you want frame rotations by the introduction of the music per meter mixed with.
Wolfgang Wieland: The delectation symmetry that we naturally have on the narrow hyper surface and this is an important observation, because it is a geometric understanding provide you get the script I we have quanta for.
Wolfgang Wieland: geometrical service geometric boundary of servers and, furthermore, the person brackets for the.
Wolfgang Wieland: Order radiative modes unchanged they're not either by the addition of the music, I mean this is of personnel that are surprising me very well know that the map that brings us from.
Wolfgang Wieland: ADM to Africa variable variables is economic transformation, so it should not change commutation relations for.
Wolfgang Wieland: radiate if degrees of freedom, but it may very well affect the face face of the animals.
Wolfgang Wieland: And this leads to new representations of quantum geometry that are, however, consistent and coherent with previous results achieved thus far.
Wolfgang Wieland: Where to go next so next we want to understand the, of course, the quantum states and just like there's a hierarchy of.
Wolfgang Wieland: classical face basis face face for the corner data face face for the radiative data also physical states will depend not only on the radiative data but also on the corner data.
Wolfgang Wieland: And they are, and the generic such state will be entangled between radiation corner corner data on the final cross section and the initial.
Wolfgang Wieland: Cross section of the novel slap under consideration, and the idea, then, is to build amplitude by doing this, this boundary states on our hyper surfaces together for forming some sort of.
Wolfgang Wieland: spin foam geometry, and they go ahead, is to understand how this fits together with previous results in.
Wolfgang Wieland: A loop loop on where we're at and spin forms Furthermore, if we look at specific radiative data such as increased impressive gravitational waves, we can, I think, learn a lot about how to realize this such form like description.
Wolfgang Wieland: From gluing such individual building blocks together and these fields, also upon earlier earlier works of mine, thank you for the attention and my apologies for the technical problems in the beginning, thank you.
Laurent Freidel: Thank you over gang same thing here when we prep for the next token there is.
Abhay Vasant Ashtekar: yeah.
Abhay Vasant Ashtekar: yeah I will could minorities ocean.
questions.
Abhay Vasant Ashtekar: Can you go back to your area quantization slide I think might be sick, so I forget now.
Yes.
Abhay Vasant Ashtekar: yeah.
Abhay Vasant Ashtekar: Now next part.
Abhay Vasant Ashtekar: Of that is this one.
Abhay Vasant Ashtekar: yeah so the two issues that I am yeah is the action i'm confused on why that is an action in the barbaric visiting is somehow you're using.
Abhay Vasant Ashtekar: Complex supply the connection or something like that or it's not so good.
Abhay Vasant Ashtekar: All right, good.
Wolfgang Wieland: Thank you, let me clarify So what we have here is.
Wolfgang Wieland: The this is so, they actually is real so and i've written everything in terms of as an SMC self to a variable so effing ab it's just a curvature of the sexual connection the complex article on actually if you wish, and seek maybe it's the sexual part of a big the action is really.
Wolfgang Wieland: and
Wolfgang Wieland: Really immersive how me.
Abhay Vasant Ashtekar: And then I mean.
Abhay Vasant Ashtekar: First of all, I want to say that you know a lot on the body can you read your beautiful talks very, very nice, thank you for that I should have started with that, but but.
Abhay Vasant Ashtekar: The issue here is about universality of conversation at a conversation and we.
Laurent Freidel: Can we can we postpone that to.
Laurent Freidel: The discussion because there's a delay, and I think it's an important question, but just just I want to keep the flow so, then we have the full picture is that okay with you.
Laurent Freidel: If it's not just.
Abhay Vasant Ashtekar: Okay, just about the fact that that isn't the spectrum different clear from the spectrum, that the market share screen of jpg or PNG.
Wolfgang Wieland: But this is.
Wolfgang Wieland: A different offer, so this is the area flux i'm speaking about the area flux operator, which is, which is related which captures the.
Wolfgang Wieland: Also, the orientation of the null hypothesis, so you can think of area in different ways, you can think of it as a density, then it is just a measure that you give me two dimensional surface or form, and if it said, if you understand it so differential form, it is, it is.
Wolfgang Wieland: It knows about orientation and the two are related by ID by different ordering in quantum theory, so one is the it's like once taking what is square root of J times J and the other one is it's just a different ordering of the same operator and one ordering allows you to take.
Wolfgang Wieland: To take to to quantifies area, taking into account that is that the normal hyper surface can have different orientation and our definition of area is.
Wolfgang Wieland: is one that is an absolute value that were orientation is cancelled out and quantum mechanical Lee classically the only differ by assign quantum mechanically they they.
Wolfgang Wieland: They have different spectra now, of course, the question is, how does this affect the physics so which notion of area is relevant for.
Wolfgang Wieland: For black hole and entropy or which one is relevant for understanding what happens if.
Wolfgang Wieland: Radiation process and our hyper surface and we want to understand how we are changes from one section to the next, this question can be only answered by franchising the full system so it's a question that cannot be answered at this.
Wolfgang Wieland: by looking at the clock to ask what is the right notion of area is meaningless without also understanding that the physics question to be asked in our words to understand.
Wolfgang Wieland: How this notion changes.
Wolfgang Wieland: Under under.
Wolfgang Wieland: Under area flux, but I think, important very important question and we don't know yet which they could both be useful, both for different questions that's that's my and it's important to to have more.
Laurent Freidel: Thank you.
Laurent Freidel: Can you can you probably can you stop sharing.
Abhay Vasant Ashtekar: Okay.
Daniele Pranzetti: Okay, so you see my pointer.
Laurent Freidel: Yes.
Daniele Pranzetti: yeah OK so again, thank you.
Daniele Pranzetti: For the opportunity to be in this panel it's it's really a.
Daniele Pranzetti: very nice to be able to present the results of the last few years and put into context what's what would work are the people that group.
Daniele Pranzetti: So what we saw so far is that the goal is to provide them a description of quantum geometry by understanding nature of the corner symmetry algebra in the case of gravity.
Daniele Pranzetti: Now, the emphasis on the corner symmetry algebra is motivated by the lessons and insights actually coming from a fuji.
Daniele Pranzetti: In fact, one can see the entire space as a particular example of the disk utilization of the corner space, which in general can be labeled by a bigger set of numbers.
Daniele Pranzetti: So forming a similar strategy, we can one can decompose the mark of space times into a collection of Sub regions and then attach a symmetry are direct to the corner, which sub region, then the coordinator space.
Daniele Pranzetti: forms in the reusable representation of of this law policy military algebra.
Daniele Pranzetti: And the choices of states in this in this space encode the quantum Germany, so this is what we saw so find the token mark.
Daniele Pranzetti: And this, so this leads to this picture of a space as a network of bubbles, now that true limits the one can take so one can shrink this single bubble put limescale.
Daniele Pranzetti: and consider, for instance, a surface a puncture surface with public sources of curvature and potion.
Daniele Pranzetti: And this leads to a position of a pumpkin geometry states as networks of surface charges, leaving on a freakin tubular version of equities be networks, which is this figure here.
Daniele Pranzetti: And this form a power of a castle he charges around each puncture which include degrees of freedom associated to.
Daniele Pranzetti: Freedom from are feasible if you want space like local space like translations and there are different truncation than one can take to recover the standard.
Daniele Pranzetti: spinner picture or possible generalization that have been proposed now going in the opposite direction.
Daniele Pranzetti: Namely, a push in the bubble to infinity one can show that the corner symmetry group contains the bms group of symmetries of infinity as well as.
Daniele Pranzetti: possible extensions that have been proposed in the literature, and this is the limit, I want to focus on in this last part of the panel, and the reason why.
Daniele Pranzetti: This is this limit is interesting is that recently were revealed an unforeseen connection between the symmetry of infinity and properties of scattering and us in the infrared.
Daniele Pranzetti: So I will review this equivalents and how this intimately related, in fact, the validity of the same Tajikistan equations and.
Daniele Pranzetti: From this and we tried to argue that there are lessons to be learned in both directions, so let me, let me start so in order to unleash the.
Daniele Pranzetti: The full power of symmetries, we need to understand, first, what is the food group of seniors which is compatible with the parents definition of US input to be fed space types.
Daniele Pranzetti: Now, building on the seminar work of the bms first and then our bond stronger and as well as more recent board where a generation of this group was proposed, we recently.
Daniele Pranzetti: proposing new extension that we call the by dms group or the bmx regrouping now the bms w group is defined as the group of receivers different systems that preserve the born again fixing and set up.
Daniele Pranzetti: more relaxed boundary conditions that originally proposed by bms were, in particular, both the former class and they can form a scale of the 2d.
Daniele Pranzetti: symmetric is allowed to bury now this group represents a subgroup of the standard consumable in that preserves the knowledge generator of scribe So this is the group mark mentioned before, and this is.
Daniele Pranzetti: The subgroup of course for specific choice of hs hs which he actually so important to notice that there is in fact in a magical subgroup.
Daniele Pranzetti: Which is for my this blooper so the group has this.
Daniele Pranzetti: semi dynamic Vanessa structure here, and this this first two factors in this part similar product represent the kinematics of groups on what mark was connecting mega some group, and it will play a role in an important.
Daniele Pranzetti: Important in a second, but the main thing I want to stress is that this is just a subgroup of the of the general course he put that you have a final distance when you push their disposable wi fi.
Daniele Pranzetti: So.
Daniele Pranzetti: Now, one of the of the useful aspects of this book is that it allows us to derive this in podcasting equations.
Daniele Pranzetti: Using uniquely a single argument so more precisely first one identifies the corner charges which are concerned in the radio space as the primary fields.
Daniele Pranzetti: For the kinematics sudden some cool features, my primary field, I mean a quantity.
Daniele Pranzetti: Which are they not here with all which is level by two numbers there's a delta, which is composed come from a dimension, and there is as which has been which transforms on ingeniously in this way under the action of the homogeneous subgroups of these two objects.
Daniele Pranzetti: And then, then the conversion rate data and the charges which I missing here, so the first tool sets are the relative data, and then we have discovering charges so we see, there is a notion of complex mass which one can build out of.
Daniele Pranzetti: The usual body mass and the dogmas So these are the current version of those charges, then there is the.
Daniele Pranzetti: Again, the client version of the angular momentum that people are probably familiar with.
Daniele Pranzetti: But in addition to that, there is also a new chart, which is a spin to charge that appears, at the same order in the magic expansion.
Daniele Pranzetti: and which also plays an important role, and there is an initial symmetry associated with this into trial, which has no local structures pride.
Daniele Pranzetti: I want to thank to say much more about this, but if it comes up in the discussion, I can comment on that.
Daniele Pranzetti: So the importance of vision, then, is the fact that they are synthetic equation that's an equation can be reconstructed by identify the combinations of this kalina observable and their derivatives that transforms homogeneous Lee under the food bms who.
Daniele Pranzetti: They saw and then one can can work out this combinations and they take this compact form here, so, in other words what i'm saying is that one can reconstruct one can understand the US in particular solution equations as into pointers for default bms w group.
Daniele Pranzetti: And then, a key aspect of sorts of the fact that this flexible and snows are equivalent today self govern teams and this i'm going to talk about this in the second part of the talk, but before doing that, let me try to.
Daniele Pranzetti: To produce some lessons that can be drawn from from the fpga experience so as as.
Daniele Pranzetti: As I show you like this input, you should question can be understood as enterprise for the investor group.
Daniele Pranzetti: And this resonates a lot with the main lessons of acuity which at its core consists of a new way of them.
Daniele Pranzetti: To think about the compositional the gravitational field in terms of representation theory structures related to the quantization of this image group associated to sub regions in this case for in the usual case it's sad to flexes, but it can be like a big.
Daniele Pranzetti: So, within this program then at the dynamical level, one can envisage a description of an arbitrary signal as a succession of.
Daniele Pranzetti: gravitational forces and each REP a fundamental button transition process at consecutive essence of time along scribe.
Daniele Pranzetti: Now, this leads to the notion of important waves, which are except solutions of the vacuum I some equations and possibly a basis to describe the additional radiation number two, but every ad infinitum.
Daniele Pranzetti: So at the quantum level, one can construct in the medical space with based on the representational labels, corresponding to the equation orbits of the concert charged in the interactive space.
Daniele Pranzetti: And then in position of simply dynamics can be threes in terms of an emotional being the pointers between the reusable representations of the charges and the quantum numbers which are associated to this important with basis.
Daniele Pranzetti: A second lesson that as as we mentioned reading books is the fact that as mark reviewed the different formulations of gravity reveal and activate different sectors of the corner symmetry group.
Daniele Pranzetti: And the first order formulation which is the starting point of Deputy quantization is fundamental to reveal the existence of this duel must charge.
Daniele Pranzetti: In this formulation, the presence of invention immunity parameter allows for a combination of the mass and the dual mass as the charge associated to super translations and.
Daniele Pranzetti: Even though I won't have time to do this, this is deeply related to the memory effects, so the basic possibility that the measurement of the displacement memory effect and like.
Daniele Pranzetti: could be affected actually by the President of a non mentioned mitzi parameter, and so that that would be very interesting window for for possible test of measurements of the music.
Daniele Pranzetti: Okay now now the second part, so in order to establish the equivalence between the synthetic symmetries in the south theorems well, we need to do is to compute the action of these charges on the share on the screen.
Daniele Pranzetti: So we want to compute this postpone bracket here where these charges i've defined this mirror charges, and I use this.
Daniele Pranzetti: computation when i'm making the peace charges to the show you before in terms of the value of their spin so s equals zero corresponds to the complex man.
Daniele Pranzetti: As equal one is some is the provider momentum plus extra terms that you need for information purposes and one go into details, and the same thing for the sprint recharge.
Daniele Pranzetti: Now, so this bracket here can be computed within the radio space by first is pressing the coordinator charges in terms of the radiative data, which are the sheer in the news conflicted.
Daniele Pranzetti: And to do that no one can use the bracket the fundamental bracket of their ad space that.
Daniele Pranzetti: By work that long ago, which takes this form here that again just simply saying that the shares, contrary to the news so in order to do this one, we need to integrate the revolution, the Cincinnati St.
Daniele Pranzetti: Lucia equations and sublingual this one needs to impose some full of conditions so again i'm not going to it is, but the basic idea is to impose.
Daniele Pranzetti: Some condition the new such that discharge aspects, they vanish when we go to Skype, especially with the came to read the vacuum.
Daniele Pranzetti: And then one can start with the normality korn ferry space as five plus minus.
Daniele Pranzetti: And then integrate we write these charges as the integral over the FLEX all along of scribe so what one does this will read the US as the q.as integrated almost cry in the news the.
Daniele Pranzetti: solution equations to suppress this quantity as a function of the sheer in the news and use this bracket to compute this person practice yeah So this is the main strategy now with this in mind let's see how it works from to connect this with the software so.
Daniele Pranzetti: Let me first review the soft garden teams very briefly.
Daniele Pranzetti: These are statements about the fact that amplitude in gravity every university behavior in the limit when the one of the of the gravitas become soft.
Daniele Pranzetti: So Omega he had the notes the energy of the gravity and this can be stated so as a factorization property of the next metrics element, including the insertion of a soft rabbit them, which can be written as.
Daniele Pranzetti: an amateur without insertion of the garden, but with some operators that act on on this magic sediment what this these different orders correspond to an expansion in Omega going to do so, this is one of the Omega is or this zero in this process and then of course correction, please.
Daniele Pranzetti: Now, in order to have a well defined scattering problem in GR one is to choose it bms pre ons quietness and one can generalize the proposal of strong injure.
Daniele Pranzetti: For service translation and argue that this.
Daniele Pranzetti: In order to do this, one excellent post an infinite number of conservation or mentioned conditions between the charger said scribe plus minus X squared minus plus what is this anti pattern matching for the coordinates on the sphere, the points on the to scale.
Daniele Pranzetti: and
Daniele Pranzetti: So, then, the existence of infinitely many matching condition, one for each point on the celestial sphere implies that there is an infinite number of concert charges and this this conservation laws implied that the charges.
Daniele Pranzetti: generate symmetries for less metrics which can be expressed as the fact that the charges commute with the as metrics.
Daniele Pranzetti: So one can then show that these conservation conservation laws are equivalent to the validity of this appearance so in order to do that it's important to note is that when we rewrite the charges as in terms of a solution insurance on Sprite so.
Daniele Pranzetti: Before that I spent before basically into a soft term which i'm going to do with us, which is linear in the shift in the in the.
Daniele Pranzetti: data, and then they said quadratic which is called the heart charge and, of course, they also actually how your corrections or your returns, which comes from the non linearity job which we can forget from now so let's just focus on this first orders and then.
Daniele Pranzetti: The going to put a space they're treating Koreans, basically, the first ingredient is the fact that the soft charge action.
Daniele Pranzetti: corresponds to the insertion of this of grabbing on on the same topic states, so it gives you is the left hand side of this of jira.
Daniele Pranzetti: Why them from the actual from the bracket of the charges on the sheer one can show that the action of the arch the heart charge on some as in politic fox single particle states is the yano and so.
Daniele Pranzetti: These are akin states for this our charge and the alien values correspond exactly to this soft factors and that's how you record it right inside of this.
Daniele Pranzetti: Of this of theorem and you have to give all the different orders, so this way the software, we are simply statements about invariance of the matrix under this even dimensional cylindrical book and the synthetic so equations are equivalent to the word identities associated to the signatures.
Daniele Pranzetti: So let me conclude with some lesson, now that we can draw from this picture for refugee.
Daniele Pranzetti: So this equivalence between the synthetic as equations and the matrix elements of the synthetic charged conservation law so just.
Daniele Pranzetti: A possible way to test the imposition of quantum constraints in a local sub region, so what we're proposing.
Daniele Pranzetti: is represented by constraints as conservation nose for the local corner charges which are associated to the boundary of a given sub region falling away, this is the example that we have from their situation balancing in refugee.
Daniele Pranzetti: And at the chemical level there are preliminary results in this direction that come from the study of representation of local space like translations and internal search to see charge action.
Daniele Pranzetti: For a lot of Sub region, which are part of this Citigroup.
Daniele Pranzetti: And from these then The hope is that one can study of what kind of constraints they associated warden identities impose on this information to Dudes with the goal to elucidate further and to understand better the connection between the canonical in the current quantization.
Daniele Pranzetti: That we have and I stopped here for for the presentation, thank you.
Laurent Freidel: Thank you, the newly so if there's any clarification question for the.
Laurent Freidel: Okay, if not let me wrap up the presentations before opening of the discussion so you can stop the video i'm going to share.
Laurent Freidel: You know, unless slide.
Laurent Freidel: Okay, so this is, you know what I promised in the beginning, and we see all these framework, and you know the supposition do.
Laurent Freidel: The linguistic continue and our teams with yes metrics results so there's summary of the discussion so we try to you know highlight one of the key points of each of the speakers there so so from mark.
Laurent Freidel: We have seen that you know imposing the constraints and internal constraints different strains gauge constraints.
Laurent Freidel: You know, on the state's means that those networks, you know that are the state that cut this surface is corner surface.
Laurent Freidel: so that you know display network states in the ballot the carries when you cut enough representation of the corners symmetrical.
Laurent Freidel: Okay, and this is a universal statement about game theory.
Laurent Freidel: And that means that you know the presentation, they carry is not only local issue so issue, too, is part of that evening and Z parameter is non zero dvm easy planetary zero there's no local issue too, but.
Laurent Freidel: that's not that's not all there is other component of that group that are very important to understand the status of quantum geometry.
Laurent Freidel: In particular, you know the the form of ISM on this year, which is a key component in the group and more as mark explain.
Laurent Freidel: Okay, so from for gang we understood so mark gave us the kind of kinematic or picture, so now from voguing we understood that you know, of course, we have to understand all these.
Laurent Freidel: You know charge evolve and and the way to do it is really we were going to melt surfaces and and what's interesting, there is the fact that the dynamics along no surfaces can be recast as a charge of evolution.
Laurent Freidel: And, and the fact that discharge evolve is you know, due to the fact that there is an ideation so ideation is now.
Laurent Freidel: encoded into the Charles known conservation and some other these these generalize this notion of july's memory effect that the presence of ideation changes the.
Laurent Freidel: Presentation of the charge, which was also described by the newly.
Laurent Freidel: And now, from the nearly we understood and we we got the realization of a very important ID, which is the fact that, yes, my takes which is like you know the speed from an opportunity, if you want, for your time space time.
Laurent Freidel: satisfies an infinite sets of one identities and, of course, you know we expect cavity to be symmetric under under.
Laurent Freidel: Under the these these countries and the ability to better reflect that So if you take states that are not symmetric then, of course, you need to correct that are made sure that the employee to really correct that.
Laurent Freidel: And this, this is the meaning of this word an entity is what identities essentially tells you that the the employee to your computing yes metrics you know carries a presentation of these.
Laurent Freidel: cemeteries in fact commute with the action of the symmetries and, of course, what we're looking for what are these metrics as the amplitude you know for the biggest.
Laurent Freidel: Sub region of all the biggest cause of diamond but.
Laurent Freidel: You know we're looking for to similar conditions on the screen from amplitude and what it gives us a really hope once we understand because we started to understand how this.
Laurent Freidel: Symmetry acts on the States, then we can use that constraints, the dynamics and instead of us having to guess what they could continue minutes of the dynamics, you can constrain the dynamics by symmetry.
Laurent Freidel: And to finish, I want to you know mention here a lot of people that you know i've been contributing to this new developments.
Laurent Freidel: Here, and you have heard from from three of them, so thank you very much, and let me open the room for questions and discussion at that I would rather start with let's say younger people junior people if they want first and then we'll go to more senior people.
Marc Geiller: share the total slides, and then we can move through.
Laurent Freidel: yeah.
Laurent Freidel: Okay.
Laurent Freidel: So you are timid yet.
Laurent Freidel: anybody wants to start.
Abhay Vasant Ashtekar: softball.
Laurent Freidel: yeah okay.
Laurent Freidel: Well, maybe, let me sorry Jose you were the.
First.
Laurent Freidel: Okay hank.
Hank Chen: Oh ask a question first.
sure.
Hank Chen: yeah, thank you for the.
Hank Chen: very interesting talk.
Hank Chen: very interesting talks own to ask a couple questions which I don't really know if it's completely irrelevant, because I see a lot of parallel.
Hank Chen: Of this corner charge stuff with essentially why know from extended topological field theories, or just feel theories, in general, where extend it means that you go one level call dimension down, and there the formulation is to assign, for example, category to call dimension to.
Hank Chen: manifolds coordination one medical to do still have the same like you you're saying the state space and then on the whole thing you have an invariant, for example.
Hank Chen: So here, I guess, the proposal is to assign the representation category right of the corner signature group.
Hank Chen: And that's where the customer, the algebra stuff comes in.
Hank Chen: So Mike my question is, what do you assigned to the.
Hank Chen: faceless, what do you assigned to this to the to the stigma right that the spatial boundary right let's say I have two.
Hank Chen: corners SNS prime.
Hank Chen: And then consider, for example, a 3D like we're up to the SNS prime and I have a 3D or ISM between them Sigma writes a special slice so what what do I sign there.
Laurent Freidel: Maybe I can take these these questions, since I worked.
Hank Chen: In.
Laurent Freidel: It and you're right initially you know part of this picture and also energy was inspired by security.
Laurent Freidel: So you know it's not a surprise that the same structures appear here the difference in the key the key challenging activities to understand.
Laurent Freidel: First, what is the nature of that group, and then you know that the fact that it's not apologetic or there is there is local degrees of freedom and therefore there's radiation so.
Laurent Freidel: I think both Donnelly and Wolfgang give you a picture of you know what happens somehow you know vacuous states are labeled by our presentations.
Laurent Freidel: And then, and then you know, on the time evolution, you have transitions and on the supplementation so so now, you have to encode the ideation in that way, something that you don't have to do for dq F T, so it is, it is similar but much more general.
Hank Chen: Yes, yeah.
If if.
Marc Geiller: If you're right, I mean it's an observation right in the sense that.
Marc Geiller: The initial idea is exactly the same right in in in a teacher if you start with something which has no degrees of freedom its innocence trivial.
Marc Geiller: But then you start to ask what happens if you put defects inside and then you realize that you have to label the defects by something.
Marc Geiller: And they are precisely labeled by what you would get if you were to cut open your topological few so they're precisely labeled by all these types of boundary data that can.
Marc Geiller: That can appear so it's exactly the logic that we're using here, except that doesn't all said here it's more complicated because you can have actual degrees of freedom which you have to keep trying.
Hank Chen: I guess it makes sense because in this geometric theory in the topological case I know that we can just keep cutting.
Hank Chen: Right until we get down to laser dimensional stuff points and then everything becomes a very simple, but here that's not the case right because you have like you have to keep track of.
Hank Chen: fluxes and radiation said, like every time you could go to do that and they're all local and you can kind of just.
Laurent Freidel: But I would expect, as part of the ideas.
Laurent Freidel: That, if you continue to cut at some point, and you have proven that there's a quota area, then you know, at some point, your your fundamental building block is going to be simple and hopefully find dimensional.
Hank Chen: Right, the.
Wolfgang Wieland: idea is basically to look at an elementary in policy way, for instance, that.
Wolfgang Wieland: Is a defect in the in the metric that propagates at the speed of light locally, now we cannot super in in classical general relativity we cannot arbitrarily super impose such.
Wolfgang Wieland: Such plane from that gravitational waves, but would be, can the proposal here is to to build the amplitude by doing it in small enough regions individuals such such defects that there are still representing.
cobblestones at the local level.
So it's like.
Wolfgang Wieland: gluing together defects that propagate a cook locally like gravitational waves and then can scatter at kota mentioned two surfaces and then certain conservation laws have to be satisfied for all charges that these defects carry.
Laurent Freidel: OK The next question is Jose and the question is you.
José Antonio Zapata: know you know so it's a first comment that said very nice extensive.
José Antonio Zapata: body of work.
José Antonio Zapata: In particular, I like Marks presentation, all the other ones too, but too much presentation I didn't.
José Antonio Zapata: get any references, or almost any references to for me would be fantastic if you will, complemented with some references.
José Antonio Zapata: I guess it's kind of difficult to to to see where to start to to see this to study this word.
José Antonio Zapata: Yes, yes.
Marc Geiller: I did, I chose here to mention at the bottom, we see people who did not kind of contribute directly to this thing so that's what I.
Marc Geiller: yeah.
Marc Geiller: If I may.
Laurent Freidel: I may, I mean it's a bit of advertisement, but if you look at.
Laurent Freidel: You know the edge mode for gravity.
Laurent Freidel: Number one, the people have more than nearly and then in there, you will have in the intro, you will have an entrance point for where we'll decide these are together That summarizes what mark does.
José Antonio Zapata: Okay okay.
José Antonio Zapata: it's great.
Laurent Freidel: contains a kind of a wrap up and summary of.
José Antonio Zapata: Just so they could, the question is about.
José Antonio Zapata: All the different options we got here for for participation or actually normal position, for it was more similar options for the array in classical theory that.
José Antonio Zapata: From all your points of view are known to be a given length in some senses and now that.
José Antonio Zapata: For essence of all the corner instructor sing to to leave in quantization to to be friends in a given and conversations, as was mentioned, but my question is, what about the classical level is there any story of.
José Antonio Zapata: A how do they differ at the classical level the this corner structures and could you.
José Antonio Zapata: say in this system.
José Antonio Zapata: If I install it is saying I need to use this point of view or not this other one being corrected something like that or does your question.
Marc Geiller: yeah yeah indeed for for some at least four, so there is no full kind of classification of what was, I mean there's you know infinitely many classical.
Marc Geiller: formulations of gravity, so there is no complete classification, but for some of them, I think we understand fairly well.
Marc Geiller: Are the differences, for example, between the metric formulation and the tetrad formulation the.
Marc Geiller: end it was already predates our work even because this has been used, also by by and Thomas team and the students to study you know the.
Marc Geiller: syntactic structure on horizons and so there is there a detailed understanding of the type of boundaries and practice structure that appears, so we say that classically for that had anything gravity, this is fairly well understood, there are also nice recent papers by simoni and.
Marc Geiller: And or bath or a very that's the effect of tech viable on boundaries.
Marc Geiller: So these are.
José Antonio Zapata: Here was presented, like your puzzle pieces of space time with your show delusional boundaries and these level, the differences are like non essential and we will propagate to infinity or something so.
Marc Geiller: Well, I wouldn't say that there are non essential, I think it depends on what you want to compute so to became mentioned these traditional boundaries for calculations of entanglement entropy.
Marc Geiller: which typically in general volatility is I.
Marc Geiller: Think, at least as far as I understand, this is we don't really know how to do this.
Marc Geiller: Unless we go through some proposals that people have in very specific models like two dimensional or it is if he were you have some prescriptions to.
Marc Geiller: To solve this, but other than that, if you look into other gauged theories, then it's when no one understand very precisely why, when you compute, for example.
Marc Geiller: entanglement entropy you actually see contributions from the surface molds or edge nodes or sort of edge states which leave on these financial boundaries or crutch across richer computing entanglement entry.
Marc Geiller: So so that's why I also mentioned on the first slide why this is also important, even if you, you have no real physical boundaries.
Marc Geiller: And, for example, insurance angles theory or in comments matter, this is a people understand fairly well how to.
Marc Geiller: How to do this.
Laurent Freidel: Maybe if I cannot because you were questioning about question about addition is that in some sense, you know what's going on is that the more charges, you have.
Laurent Freidel: The charges are kind of a window, you know, there are like the globe theoretical window onto components of the metric projected on your on your corner and, of course.
Laurent Freidel: The bigger the charger but the more charges, you have the more information, you can gather.
Laurent Freidel: Around that so the more control, you have on your theory and then it's like the difference between the metric and the.
Laurent Freidel: And the let's say first order is that, for instance, you have an extra conservation over there, which is the Gal slow right.
Laurent Freidel: which you know dive in the metric case and the gals know, of course, if you give me a frame here, and you think radiation.
Laurent Freidel: That will be you know, and you pick something that will be a kind of a frame rotation you to the presence of ideation so you can you can access that that extra charge to to have a little bit more information.
Laurent Freidel: The different seems to be really at the quantum level, except maybe this is questions around the jewel mass media, the parameter so.
Laurent Freidel: Ultimately, you know, we would like, give me the biometrics are low energy by Marina classical action, it should be observable and the semi classical level so.
Laurent Freidel: You know that that's kind of the challenge there, you should be able to see a difference or measure, but you know it's not done.
Daniele Pranzetti: A quick comment, just to wrap it up at the classical level, it also depends like which kind of boundary conditions you're interested in, in the sense that.
Daniele Pranzetti: If you want to impose certain specific class boundary condition on a given boundary for whatever physical reasons you're interested in that will affect.
Daniele Pranzetti: The form of the synthetic potential and he will give you access to maybe a sub sector of the food or a specific part of the current signature group rather than other, so there is a.
Daniele Pranzetti: Very clean connection between boundary conditions.
Daniele Pranzetti: choice of money regression that you use to impose upon the conditions and the sector of the consummate reactivity you have access to based on the corner of the boundary condition that you are interested in so that.
Daniele Pranzetti: That can determine if you want one which representation activity which not.
simone: And even if the sector is the same, the actual presentation of the charges, we change by changing these boundary conditions right.
Daniele Pranzetti: yeah it can.
Laurent Freidel: set a question.
Seth Asante: And, yes.
Seth Asante: hello, and thank you for the Nice and.
Seth Asante: yeah I have a question about about a country geometry from these surgeries and so maybe maybe I didn't understand it clearly so you can tell, but so far I see is that the.
Seth Asante: Continuation of air variables appearing from all these different formulations and but also education, he from the continuum Rachel from mtg already has these.
Seth Asante: Continuation of variables, so my question is like what new trends do you see from the local edition of his estimation, as a stress fractures from the from the continuation of these symmetries like what sort of new structures to the add to the 10th we already know from.
Wolfgang Wieland: So he.
Laurent Freidel: knew I mean, can I first started I think it's easier if you look at the corners imagery or presentation of mark.
Laurent Freidel: You should decide now.
Marc Geiller: So.
Marc Geiller: If you if you really want to know but.
Laurent Freidel: More the next one yeah this one, so the thing which is now possible and mark and command on it, is that these.
Laurent Freidel: bracket between the metric component can be derived purely in continuum quantum theory right, this is a semi classical bracket.
Laurent Freidel: And, and so the quantization come from the quantization of that bracket the colonization comes from the colonization of these degrees of freedom, whereas in the conversation photos from the assumptions that you have underlying discrete states which are loops.
Okay.
Laurent Freidel: Maybe Martin, you know.
Wolfgang Wieland: It is the statement I think that the like the way I like to phrase, it is that in any so to have the sweetness of area is not tied to using spinners it is, it is something that we can see.
Wolfgang Wieland: From a more.
Wolfgang Wieland: The more general way, and in fact this in my, in my opinion, this is a very strong statement because it says that.
Wolfgang Wieland: That it's independent of the representation in there in the early days of recording gravity there was this idea that it should be possible.
Wolfgang Wieland: This loop representation to go from SP network representation to the okta representation weather.
Wolfgang Wieland: Where you better be considered we've states or other states.
Wolfgang Wieland: or shadow states and.
Wolfgang Wieland: That and and what we are developing here goes into this direction to have this to to have.
Wolfgang Wieland: To to understand the sweetness of area in different.
representations of your quantum states.
Daniele Pranzetti: complimentary.
Wolfgang Wieland: description that made them access.
Wolfgang Wieland: Observers that are otherwise invisible in the spinner for presentation.
Wolfgang Wieland: And then, a more handy way to go directly to the related degrees of freedom and understand how the two couple together how, for instance area changes under the.
Wolfgang Wieland: Under under under the how the Cross section of not surface changes, depending on the incoming radiation, of course, there is a caveat so already in flight space does area change in if you're just have a light Cone in in.
Wolfgang Wieland: In makovsky space so it's so this charges capture or the change of these charges will not only consider radiative modes, but also.
Wolfgang Wieland: geometric degrees of freedom that that tell us how area, for instance, a lot of charges change just by the dynamics, or just by the kinematics of flat space.
Seth Asante: thanks for the expensive and.
Laurent Freidel: Any other questions.
Hal Haggard: build on oh sorry about you can go ahead.
Abhay Vasant Ashtekar: No go ahead, but.
Hal Haggard: I just wanted to build on seth's question a little, we know that.
Hal Haggard: That, in addition to thinking about area there's there's interesting questions of shape matching if we want to glue sub regions together, and so I am curious if the boundary symmetry algebra tells us something about.
Hal Haggard: This shape matching.
Laurent Freidel: Oh yeah can I can I take it i'm.
Laurent Freidel: really glad.
you're asking.
Laurent Freidel: This question so.
Laurent Freidel: Because.
Laurent Freidel: yeah In fact I think he totally totally see the picture of the network, which is twisted geometry so there's two pictures of the network, one is that it's.
Laurent Freidel: it's a collections of network and the twisted your image be is a little bit different is that you have a collections of nodes and you have gluing among them like you know cells that you're doing they're kind of equivalent, but you know they're kind of.
Laurent Freidel: Different in their in their philosophy So here we are more in the in the context of twisted geometry and, as you know, there's a result of you.
Laurent Freidel: Know gang Gallo, where where you know, there was this puzzle that twisted geometries or not legitimate shoes right and.
Laurent Freidel: There isn't a difference that not only when you go to edges you're using a rotation, but you need to use the next time I felt warm up.
Laurent Freidel: Right and and and this I said to a mapping, it was was necessary to kind of understand the gluing of this twisted geometry, now we can tell you Oh, we understand why you need us to send to our map it's this it's the tangential metric.
Laurent Freidel: Right, so the Nice picture of veggie that edge is missing is that it assuming that once you know the edges, you know you can have know the the geometry inside and and this isn't war is not there, so there's.
Laurent Freidel: A direct connection between I think the security and also the software that whole gang is talking about.
Laurent Freidel: And and and the twisted geometry that that would really be useful to develop right so that that that, because that is sent to our as we are just arguing is really.
Laurent Freidel: The core radiation okay transition, so I think there's a there's a formidable opportunity there for the steam form to kind of go back includes you know.
Laurent Freidel: A little bit more data like this, this is at war in the in the making, and also the vector n that we see there the normal you know, to make it provides.
Laurent Freidel: Does that answer.
Hal Haggard: yeah.
Laurent Freidel: You can you can record for people who are not experts of twisted geometry where where this is where you know wasn't came about.
Hal Haggard: yeah but i'm also just interested, it seems to me that you guys have more than just that, because you have also the the normal direction, as well as the tangential direction.
Laurent Freidel: Yes, yes.
Hal Haggard: Yes, what I should what I should learn about that normal direction.
Laurent Freidel: Yes, I think, I think that that's that's The next step, so the normal direction is that the twisted geometries industry to context where you have a fixed frame.
Laurent Freidel: But we are lacking, you know, there was always a mismatch between energy and speed for most been from contains SL to see and and speed networks don't so, so I think you know, the introduction of these normal as part of the face base is the key to allow.
Laurent Freidel: an essay to see a presentation on on locality states right and then.
Laurent Freidel: I think, then you can think about an extension of the twisted geometry where not only you have the self who are doing mismatch but also understand how it's kind of embedded into a for the geometry right so.
Laurent Freidel: These are you know things we we we say people should we invite people to do a few years ago, and I think they're still there still there, I think.
Laurent Freidel: it's clearly you know, the door is open for energy to kind of complete the the picture and and erase completed the difference between speed networks and pitfalls.
Laurent Freidel: With the additions of this extra information.
Daniele Pranzetti: yeah In fact I mean just a brief comment on that them, so the inclusion of this.
Daniele Pranzetti: Internal Norman.
Daniele Pranzetti: Faith based on what we saw in one of the series of paper is that it tells you that you start from not.
Daniele Pranzetti: Lawrence algebra but the suffering upon K algebra include this normal and then, once we impose this mpc constraints you go down to.
Daniele Pranzetti: Essentially, see so instead of having a set to see in person is in physical constraint and going down to us to chew you have a bigger symmetry algebra which.
Daniele Pranzetti: Once it was the same physical state you end up with a central see so the central see charges all there even after you're imposing constraints, if you include this internal normal interface base.
Daniele Pranzetti: And that's how you can see, in fact, that then this revelation and mark with their their their form it towards a customer of this SF juicy.
Daniele Pranzetti: So it's completely compatible with the food Lawrence invariance this dispensation of the area that emerges from this picture if you include this extra variable in your court in your in your boundary in your corner office space.
Abhay Vasant Ashtekar: Okay, can I just say a couple of things.
Abhay Vasant Ashtekar: First of all, I mean I know this is, I think that all our panelists but it's basically this Panel has been extremely successful I mean you guys did a great job, so thank you very much for that.
Abhay Vasant Ashtekar: I mean, I think this whole idea about.
Abhay Vasant Ashtekar: You know, looking at the kinematic the symmetry group and it's a presentation so i'm looking at the whole physics and after that and how much we can get and how much on what you don't get etc is exciting.
Abhay Vasant Ashtekar: But I also feel that there are some some things that need much more careful thinking which I think has not been done so far.
Abhay Vasant Ashtekar: And, especially in the context of this last Daniel is talk about the bms group, and so on.
Abhay Vasant Ashtekar: So, for example, this magnetic charge right, and I mean when I looked at long time ago, the net charge and, of course, we know that the not for momentum is absolutely consider it cannot be.
Abhay Vasant Ashtekar: radiated away but not super momentum could be ready get away, and there is no no problem with that.
Abhay Vasant Ashtekar: But the point is that, is there going to be a magnetic memory and there are reasonable papers, where it came from people now, which show that.
Abhay Vasant Ashtekar: Unless you a beacon your boundary conditions enormously about the condition the initial data and we're just talking about the vacuum situation right now vacuum solutions, which is what we're looking at here.
Abhay Vasant Ashtekar: That there is no magnetic charge, I mean there are particularly the paper by word by media beauty, which shows that.
Abhay Vasant Ashtekar: Under the you know, Chris to try them and kind of or even slightly weaker versus have heard of that that that there is no magnetic charge.
Abhay Vasant Ashtekar: So I didn't know magnetic memory, so I think one should be little bit careful about.
Abhay Vasant Ashtekar: making statements of my goal, and so on, and.
Abhay Vasant Ashtekar: The second thing is that, even if.
Laurent Freidel: The software only be say or is connected.
Laurent Freidel: I would, I would tend to agree there's no magnitudes is same thing that there's no free magnetic monopole but, in the same way that you have included with with what's happening there is that the.
Abhay Vasant Ashtekar: disappearance nobody's nothing at all.
Laurent Freidel: well.
Laurent Freidel: Let me finish maybe.
Laurent Freidel: what's happening is that it's the same thing as a parameter in two cities that whatever is the challenge that you would call the mass is kind of in the presence of a nonzero music parameter is now kind of outdated.
Laurent Freidel: Right so so what would you know where the usual people in in.
Laurent Freidel: In in gravity do is they, they work with the metric formalism gamma is equal to zero, and therefore began as equal to zero, which you cannot detect what we are trying to.
Laurent Freidel: What we're doing here, thank you Jesus, we have, we have a rotation of the other face space really be like data QC and then the question it's interesting question for us is whether you can you know.
Laurent Freidel: include that into a observation and if the answer is no, then Okay, but.
Wolfgang Wieland: I cannot say yeah.
Laurent Freidel: Seriously, yet right the same way that is a phenomenology of of the data parameter so it's kind of an open question.
Wolfgang Wieland: I agree with you, which made me a classical like that is kind of a question.
Laurent Freidel: about this rotation of charts and now the total, which we call the total mass which act as a generator of translation is a little bit you know when, in the presence of non zero gamma is the son of the mass and mass that's really what's happening.
Abhay Vasant Ashtekar: yeah exactly what.
Abhay Vasant Ashtekar: I mean, I think we're looking at classical number two if you're thinking that you're got some other to gripe about two different things, one is you can say the classical theory of general relativity formulated any variables you want.
Abhay Vasant Ashtekar: And then, what does not measurable content is not mathematically.
Abhay Vasant Ashtekar: yeah we're talking about medical.
Abhay Vasant Ashtekar: So yeah so so this file, the claim is that no I don't think that there's a magnetic charge.
Laurent Freidel: Okay, but.
Laurent Freidel: What we're saying is that we don't we don't know, and I think.
Abhay Vasant Ashtekar: I I disagree with that, so we can discuss.
Abhay Vasant Ashtekar: yeah I think the second more radical or more.
Abhay Vasant Ashtekar: statement is that.
Abhay Vasant Ashtekar: The development, the soft charges on this, you know various things that were discussed at the end.
Abhay Vasant Ashtekar: And then, again, if you look at full nonlinear general relativity the only theorems about global existence, etc, we have our materials which come from stability of Madagascar space time.
Abhay Vasant Ashtekar: And if I look at history recline among if I look at data across verticals slightly beacon generalizing a bad word which was in 2000 or if I look at the La and.
Abhay Vasant Ashtekar: Crucial which is.
Abhay Vasant Ashtekar: Like a different point of view by different groups in all those cases, in fact, that these conservation chart this is conservation have.
Abhay Vasant Ashtekar: infinitely many conservation challenges are empty, because all the total flux of super moment than one squared minus and scrabulous are identical zero.
Abhay Vasant Ashtekar: So they're just saying zero is equal to zero, nothing more it's open question about whether there is exact date they're doing this initial data which are recurring there to allow roughly speaking.
Abhay Vasant Ashtekar: of data five in one upon our term of the metric spatial infinity and then you evolve them and what happens and these questions are.
Abhay Vasant Ashtekar: Just being looked at currently and we don't have any idea about in fact by exactly is the primary in the.
Abhay Vasant Ashtekar: Current indications that rigorous people have is that in that case, in fact, even side to is not going to be well defined on Skype.
Abhay Vasant Ashtekar: And then the integrations that were being done in order to talk about you know the evil for supper moment and forgetting about the dual quantity will just not be well defined so where to be a little bit I mean we can go ahead and like, but we should always have a.
Abhay Vasant Ashtekar: little bit of a grain of salt, you know in mind that Melbourne wedeman what is one have actually been shot.
Abhay Vasant Ashtekar: i'm not even sure.
Daniele Pranzetti: yeah.
Daniele Pranzetti: Yes, I mean, I think there are two aspects of the.
Daniele Pranzetti: So one is, as you pointed out, the observation implications which I agree that one is to be very careful and.
Daniele Pranzetti: An s to.
Daniele Pranzetti: relate to what has been proven right in the past, but then there's also like the this if you want the more formal aspects that you know.
Daniele Pranzetti: These are, these are new ideas in order to eventually concise gravity right it's it's a yes, the use of this child is not necessary.
Daniele Pranzetti: yeah just eventually derive new member effects which may or may not be observed, but also for quantum gravity Community it's also to have new tools to.
Daniele Pranzetti: To impose like prison yeah a new constraints of dynamics or own understanding of the fear of the more fundamental level, and so I think that.
Daniele Pranzetti: The issue is also Okay, what is the connection with the metrics like can we say anything in terms of X minus scattering antidotes can we like suggest number two correction to be as metrics using our techniques and.
Daniele Pranzetti: enticing this algebra stuff like we would do it in that could you more than maybe in a few quantifying coupon to you.
Daniele Pranzetti: And there may be there are new options that may be may not be related necessary to observation, but my allow you to include number two effects in a framework that people usually do not to do it.
Daniele Pranzetti: right there yeah.
Abhay Vasant Ashtekar: I agree, I agree with you that we are very much.
Abhay Vasant Ashtekar: Everyone can certainly try to do it and even if things are not proven rigorously practice to see if we can get insight, I agree with that completely the problem of the medical physics perspective, I can think.
Deepak Vaid: I have a question.
yeah.
Deepak Vaid: So I missed the early part of the talk so many pieces already discussed but incidentally just mentioned the matrix and non productive directions to.
Deepak Vaid: The question is that the first of all.
Deepak Vaid: Sorry mom a little bit.
Deepak Vaid: How do you define the metrics at all in the financial picture right that's that's that's one of the questions.
Daniele Pranzetti: So it's not really.
Daniele Pranzetti: disappointed funny Desmond is a picture in per se it's more about using these ideas for instance of.
Daniele Pranzetti: entertainers as between the.
Daniele Pranzetti: Different representations as a way to to represent.
Daniele Pranzetti: Like to SAP like to stand up all possible five and diagrams if you want so like once you understand that the problem can be cast into an algebraic framework, you can use.
Daniele Pranzetti: techniques, with people using jeeves such as quantization through the national into finer to apply this to to the O P of.
Daniele Pranzetti: asthmatic, for instance, like I didn't have time to really talk about less your order number was in the name of the panel.
Daniele Pranzetti: But what you're doing slicer of is basically you take this usual asthmatic speaker in the momentum space you recast it in terms of safety on the celestial sphere, and then you use the cfd up to.
Daniele Pranzetti: The esoteric to reconstruct the only possible amplitude from symmetry constraints and and there you do it the legwork to have a look one group now what we could do is actually tried to do this number typically at all loops if we know how to how to.
Daniele Pranzetti: If you want to.
Daniele Pranzetti: rephrase the op language in terms of algebraic language so that would be a possible way to.
Daniele Pranzetti: come for this.
Deepak Vaid: Okay, so I mean all right, so I mean, I agree with the statement that entertainers.
Deepak Vaid: would be the starting point for considering any notion of metrics and engaging.
Deepak Vaid: So, given that you also agree on that, on that point.
Deepak Vaid: So, so what would be the physical picture let's say I wanted to talk about.
Deepak Vaid: The scattering of some particles for particles for Muslims particles.
Deepak Vaid: Right, with some momentum now the matrix there can be written as some function of those Mandelstam variables, for instance, right.
Deepak Vaid: So, how would How would one relate that.
Deepak Vaid: To.
Wolfgang Wieland: When.
Deepak Vaid: intertwined a point of numbers, for instance.
Daniele Pranzetti: To i'm saying you can compete so again, if you recast this picture in terms of.
Daniele Pranzetti: safety perspective, like a sorority, then you know, once you have the O P, the fundamental gop right from there, you can reconstruct the purity all possible scattering amulets if you have your before the most the most general be.
Daniele Pranzetti: emblem and things that you know P, is nothing has that, basically, if you want like a trivalent intertwining.
Daniele Pranzetti: In our language so understanding what are, what is the full structure of this in Japan, it would be.
Daniele Pranzetti: equivalent to understanding what is the full month or two, but the P, which is the building block to recast, of course, I mean this program it's not like.
Daniele Pranzetti: Totally we will define you know it's not clear if you can read recast the all the asthmatics attitudes into this safety picture, so there are different carriers one is to keep in mind, but the, the idea is to like.
Daniele Pranzetti: constrain the obe using the the cemeteries and that's an adventure 321 ties the algebra to to compute all the all the loop corrections come from it, so that that would be there if you want.
Daniele Pranzetti: The philosophy behind this.
Laurent Freidel: Then I try, maybe the parametric a year several question and you're using the first is was about going from the metrics to to this platform is that was that the question.
Deepak Vaid: Like the first one um well, I mean.
Deepak Vaid: The question, the question was that, how do you how do you think of an edge metrics in the.
Deepak Vaid: past.
Laurent Freidel: Is the lovely to yeah the way we think about is just metric is is a quantum amplitude.
Laurent Freidel: diamond and a very particular diamond the biggest diamond there is attached to it, not that's what it is right.
Laurent Freidel: For that particular diamond you can use the usual basis of momentum, etc, now that that usual basis is not available.
Laurent Freidel: So you know if you're if you're a quantum gravity person at some point, you also want to be able to attach simply to say phenomenon diamond or smaller diamond diamond inside okay so let's say.
Laurent Freidel: You know, you want to have a common picture of the biggest diamond this particular one and then all the other ones, which are inside and and so.
Laurent Freidel: The first thing is, you have to understand, for instance, that is, you know my mental state is not it's not something a generalized inside it's something very simplistic so, but what what you can do and that's that's partly what we do, but we would.
Laurent Freidel: do is to say okay well instead of labeling the subject States by this particular notion that that really flat space notion, let me label them by by objects.
Laurent Freidel: which are really quantum gravitation on and then you can replace the basis of States they bought by moment by the basis of States they bought by the charges of symmetry.
Laurent Freidel: Okay, and that's kind of part of the translation so is that without answer so you first do a translation, where you leave you let go of this notion of.
Laurent Freidel: A synthetic momentum, because you know, and you take something more non parametric Okay, which is the opposite nation that then he talked about or mom okay so once you understand that dictionaries just kinematic on change of basis, then.
Laurent Freidel: You know you have a framework where hopefully you could talk in the same way about the biggest diamond, which is the metrics amplitude and the smaller ones.
Deepak Vaid: As well okay so.
Deepak Vaid: Sorry, I can I can I just.
Deepak Vaid: get one quick tip.
Deepak Vaid: So the thing is that the law, I mean.
Deepak Vaid: Now this is something that i've taken straight from your work with living with Ezra.
Deepak Vaid: And I mean maybe you already know about it and you're considered it before.
Deepak Vaid: But so in your work, you with the Attorney showed that coherent rated whiners.
Deepak Vaid: Are liberal by points on the graph meaning.
Deepak Vaid: Right.
Deepak Vaid: and
Deepak Vaid: I mean.
Wolfgang Wieland: it's also a fact that.
Deepak Vaid: If you consider the kinematic data of the scattering of in much less particles, that is also label by.
Deepak Vaid: The same geometric object, a point in the grass meaning.
Deepak Vaid: So I mean unless I have.
Deepak Vaid: completely misunderstood something in your work, you know or lesson really like some some some ignorant error on my part.
Deepak Vaid: It would seem to me that that itself is telling us right that there is a correspondence between these two pictures scattering on the one hand and Colin and intertwined, on the other hand.
Laurent Freidel: yeah we we know disagree, but yeah yeah the I think you know what you mentioned is a result in those networks we put all of them.
Laurent Freidel: And he was suggesting we was the you know, the question was whether it was just some cinematical accident, whether there's a deeper reason.
Laurent Freidel: To do that, and what i'm describing here is a more careful program that.
Laurent Freidel: You first understand particle states as a presentation of symmetry you understand these are synthetic symmetry has been connected to this corner symmetry and then.
Laurent Freidel: Then you can match the to our presentation, so I don't disagree with your intuition, the question is whether it was you know it's the particular one which is indeed there or it's and that requires understanding what is the mission of energy and momentum for for smaller object.
I think.
Abhay Vasant Ashtekar: It continues along these lines, and I love it and I really appreciate what you said just now getting an answer to the question about that one was to reformulate what else to get rid of mental space as a mentor and one wants to select look at.
Abhay Vasant Ashtekar: The recast it in terms of observable algebra who's charges and so on, and look at our presentation, but the point is that these representations might be completely in equivalent.
Abhay Vasant Ashtekar: Make it may well be that the representation, one gets naturally from something like spend networks.
Abhay Vasant Ashtekar: is quite.
Abhay Vasant Ashtekar: is really an equivalent to the fokker presentation.
Abhay Vasant Ashtekar: And that is the reason why you know the usual.
Abhay Vasant Ashtekar: Nada normal as ability, etc, etc right, so what is needed is to understand the relation between these two things.
Abhay Vasant Ashtekar: For example, the fox representation tells you nothing about area conversation in the normal sense right if I take fox by some guy with horns, then I there's no such thing as area quantization.
Abhay Vasant Ashtekar: Now, all the gang was telling us about you know.
Abhay Vasant Ashtekar: area code zero Dom is fine for the looking at the foxy and that fucking is not what what are called the great on for proper presentation that was the pocket a presentation of the boundary degrees of freedom, which is kind of a different thing.
Abhay Vasant Ashtekar: So I think what one would like to do is too much more understand how one might be able to relate, roughly speaking very few aspects with the cooler because.
Abhay Vasant Ashtekar: I mean, as all guy was saying, even in flat space we know if I take doesn't to sphere, like the that that area is actually growing, and that is not at all growing because of the radiation going through it's not because of interaction because radiation, we just like in a magical effect.
Abhay Vasant Ashtekar: And somehow and somehow there is a but but it's more that there's also the cooler big aspect so there's a kinematic effect there's a cool lombok aspect of gravity, which I think spin networks do capture.
Abhay Vasant Ashtekar: And that there is a de de gras and we want to understand kind of relation between all three and that I think is exciting plenty for me at least.
Wolfgang Wieland: And I also agree, I would also stress that if we are if we insist that we should start out with finite building blocks and quantifies general relativity in finite regions.
Wolfgang Wieland: Then there isn't as we somehow doing in Luke calm gravity in display network representation, there is no, we cannot separate the two uniquely we cannot separate there's just no single point in in the space of the.
Wolfgang Wieland: Face face on on another type of surface that would tell us this is this is radiation and everything.
Wolfgang Wieland: else is just kinematics, but this is, I don't, this is not a problem, I think this is just this is.
Abhay Vasant Ashtekar: I get it.
Abhay Vasant Ashtekar: I get it, I get, but we need to relate this to what is happening at infinity to my content and the rest of.
Abhay Vasant Ashtekar: The law, the law and negative infinity to infinity.
Abhay Vasant Ashtekar: usual thing and physics, like me, sometimes sufficiently large region given to the compared to the scales of interest to the problem, so we need that that did with the.
Abhay Vasant Ashtekar: substitute or that'd be the next generation of what people who normally call is effective filters are low energy and we need to make that contact someone.
Wolfgang Wieland: Absolutely, but it amounts to send to.
Laurent Freidel: To.
Wolfgang Wieland: To take a limit to take a limit in there in the class, I know, clear picture, so to say, so we have a let's say colonization of finite diamonds in finance regions, and we take all classical.
Wolfgang Wieland: absorbers on the on the classical face space that we can assign to this region as quantum and the only once we have that, so this is kind of the problem.
Wolfgang Wieland: The first problem for us the primitive program, which is already hard enough, but the idea is that it's perhaps easier in some way, and then only takes the limit to infinity in order to divide you to understand as matrix scattering on on iTunes by sending.
Wolfgang Wieland: So limit within the quantum theory, for instance, by choosing Korean states to describe the geometry of the corner in a as a coherent state and then sending the this code and then start sending the expectation values, then choosing a family of such states that.
Wolfgang Wieland: That we can take the limit to infinity but then of course they will know the ambiguity may arise, so we may not get a unique folk representation out of this construction, but this is this is perhaps fine and just tells us that there is there are then in equivalent.
Wolfgang Wieland: representations EP mcs to be at infinity.
Laurent Freidel: I think that is my new point, maybe, where I can say is that.
Laurent Freidel: OK sorry.
Then.
Wolfgang Wieland: We can also ask about better, this will then be unitary better test matrix will be unitary now in in the book, we were considering that is nice labs that were always truncated assuming that then all costs okay so, then there is always that.
Wolfgang Wieland: You can think there's always this whole at the end point so we may not necessarily we may not even expect unit, the S matrix that we get out of this construction to be to be unitary and I, and I don't think that is a problem.
Wolfgang Wieland: either, because the construction just implicitly implicitly assumes that try plus y minus is not the only cushy surface oh yeah i'm not complete coaching services.
Wolfgang Wieland: And I think that is also an interesting.
Laurent Freidel: Now to.
Laurent Freidel: Where I wanted to add, is in fact the project you're you're describing which is exciting is the beauty, is it it's it's exactly what's happening right now so right now there's a you know we we understand this.
Laurent Freidel: As Matisse picture or this entity dynamics in terms of these charts, as I said, we understand better the connection between the current first.
Laurent Freidel: windows under what we mean by economic sector, and then what is the interplay between the two that's exactly what this new developments.
Laurent Freidel: are about like desires in charges and etc and that's the language that because it's connecting naturally to define it, that we can we can transfer, so this project is exactly what it is about and it's kind of them happening.
Laurent Freidel: I don't remember also about the colonization of area in if you look at what mark rights is that not right, the algebra the area operators that qq.
Laurent Freidel: And, and the thing is that this is some kind of a density, so if you want this, if you normalize the area level.
Laurent Freidel: what's happening, when you go to entities that the opposite, so the area is kind of one of the casimir of the kinematic or subgroup right.
Laurent Freidel: So when you go to infinity the casimir blows up, but if you normalize everything What it means is that the the operative specter.
Laurent Freidel: shrinks so from the point of view infinity you will never see you will never see the area spectra by design, because the area or one of the area plays the role is semi classical parameter.
Laurent Freidel: And this is why in some sense to to really fully you know access quantum gravity, you need to have you know.
Laurent Freidel: Regions which are which are not area infinite does that make sense, oh yeah we can even prove that yeah the athletics cannot see the area gap just by design, because you know you're you're taking a limit with the spectra condense.
Abhay Vasant Ashtekar: yeah not like a.
Abhay Vasant Ashtekar: natural part of, but I do worry about these things have been refined I distances costs six and so on, I mean I read all these things are too formal.
Abhay Vasant Ashtekar: Even simplest cases are costs, weeks and then none of these you know hamiltonian frameworks work and, therefore, why am I, leaving this hamiltonian frameworks, to begin with, and so I mean.
Abhay Vasant Ashtekar: there's always this tension between the.
Abhay Vasant Ashtekar: occasions when he's making and one wants to bad financial reason, but when is the.
Abhay Vasant Ashtekar: Essential COMP classical concert complications that are present at the financial.
Abhay Vasant Ashtekar: Now I think was on.
Laurent Freidel: And there's the beauty of quantum mechanics to there's many things that, in fact, you know you can worry the classical level what you were talking about the details and whatever into CD and then you bought a CD.
Laurent Freidel: And then have that appears because so because the quantum version, you know kind of takes care of itself so at some point, you know we have to leave up the about the worries once we have the right kind of transposition when we understand that the right.
Laurent Freidel: classical variable we have our handles on all these kind of face face charges, then we can you know, look at at the quantum differently.
Wolfgang Wieland: Or we can put you can ask what is it what is it costing at the quantum level.
Laurent Freidel: Here sure I mean that's yeah acoustic is i'm sure at some point we don't understand, yet that acoustic is going to you know appear as some kind of intertwine or it's going to appear in some in some structure, of course, we, we have to find the translation.
Abhay Vasant Ashtekar: very nice development, I think, well, listen to our so many great.
Laurent Freidel: yeah yeah I think we should do it okay i'm good, I have a meeting now in two minutes i'm happy to to leave.
Jorge Pullin: Okay let's thank everyone.
Marc Geiller: Thank you.