Jorge Pullin: Our speakers is Wolfgang leland will speak about observers you versus gauge cemeteries boundary observers and quality local hardworking.
wolfgang wieland: Thank you very much.
And I.
wolfgang wieland: So, before starting my talk, I would also like to thank for the opportunity that is given to me to present this work.
Dongxue Qu: I was want to briefly apologize originally I was.
wolfgang wieland: Hoping that I could speak about some new work that I have been working.
wolfgang wieland: That i've been developing in the last couple of months, but things took a little longer, and so I decided instead to speak about something some of you may have already heard in previous talks of mine that I gave, for instance, that better Meta institute a couple of weeks ago.
wolfgang wieland: In any case, I think it is safe to.
just give you.
A bit of an overview about what i've been.
Working in the last couple of.
wolfgang wieland: years, in fact, and how this fits together in a broader perspective with recent developments in various in our own field, but also in in other communities.
wolfgang wieland: In fact, the outline of my talk is the following first of all, I give a very broad introduction and motivation for what i'm doing and then.
wolfgang wieland: I will go a bit into more technical details for how to set up the problem of localizing degrees of freedom gravitation the gravitational degrees of freedom in.
wolfgang wieland: domains that are bounded by non surfaces, and the third part is a bit of an upshot for what i'm interested next, and what I would have liked to expand it more about in the in this talk, in fact, I will speak.
wolfgang wieland: about the introduction of the mercy parameter from these gnarled surface person perspective and how it affects over observers and deforms symmetries gauging interest.
wolfgang wieland: And finally, I hope that we can have a bit of a discussion about what's going on in here, furthermore, I like to stress that you are very welcome to interrupt me at any point for questions and clarifications and if you have just comments that should be added.
wolfgang wieland: If you think are important, so let's go into the into the first part, the general motivation, so what I.
wolfgang wieland: am interested in here is to understand and isolate gravitational degrees of freedom in finite domains, and then the question arises, what kind of domains should be chosen.
wolfgang wieland: should be choose and the boat, I would like to argue for is that we should think about causal regions, in other words, regions that are bounded by.
wolfgang wieland: surfaces and i've indicated that a bit in in here in this comic picture and the different views, why this is interesting, so one possibility is to think that what's going on here is a mayor mayor cage fixing, in fact, we know that.
wolfgang wieland: If you if you start out with the quantum State on a stage partially cushy hyper surface and let's call it side not.
wolfgang wieland: The role of the hamiltonian constraints to relive it equation is that it is the generator of time like if you malfeasance on Shell and that, in other words.
wolfgang wieland: States on that correspond to one hyper surface our gauge equivalent to state on that earlier heights and now you can ask how do I represent his cage equivalence class of states.
Jonas Neuser: And one possibility is to kind of push this time evolution.
wolfgang wieland: to its maximum cushy development in our words to local guys, the states on the surface itself and so that viewpoint is to say that.
wolfgang wieland: going to not hyper surfaces is basically a neat way to characterize gravitation degrees of freedom, on the other hand.
wolfgang wieland: I believe that this question is also related to the issue of course granny maybe how to build gravitational observers and go from smaller two variables that are defined in smaller regions two.
wolfgang wieland: variables that that are more course that are closer and one perspective for this to characterize this problem that comes kind of from our Community is that this should think of course meaning in terms of gluing.
wolfgang wieland: reputation and subsystems along common boundaries and then again the case of normal boundaries is kind of natural.
wolfgang wieland: Finally, there is the issue of interest particles soft modes and animals that have been.
wolfgang wieland: created a lot of interest recently from different communities, and in fact in general relativity.
wolfgang wieland: Some of the simplest observers like energy momentum angular momentum, but also charges for super translations are or Center of mass they are analogous to.
wolfgang wieland: The charges in a gauge theory to recharge aspect in quantum electrodynamics and then the question is, what is the role of these charges in in the quantum theory of gravity, should we treat them as super selection sectors as include it will be very different.
wolfgang wieland: States have different charges at infinity correspond to.
wolfgang wieland: unitary in equivalent representations, or should we try to also realize that the different super positions of this super selection sectors in in our quantum description, and this is a question not of just Mer mathematical interest it.
wolfgang wieland: Perhaps has also.
wolfgang wieland: Will.
wolfgang wieland: Perhaps it will be actually relevant for actual experiments in fact we can think of creating in the laboratory super positions of.
wolfgang wieland: Of gravitational systems to gravitate through the newtonian potential, in other words, we can think of, or more precisely because think of situations where we have.
wolfgang wieland: quantum model and a lot of the cavendish experiment, where we have a source mass that is in superposition of different position, I can states, and then we should ask how can we characterize such an experiment, how do we.
wolfgang wieland: How would we describe such an experiment in the quantum theory of gravity and.
wolfgang wieland: There it is, then, then, then the position i'm states of the source mass they are, I can state of the Center of mass, but the Center of mass is just one of the.
wolfgang wieland: sympathetic punk array charges at infinity so it seems actually necessary to consider such common superstitions of charges at infinity to characterize this particular thought experiment that may actually be realized in in in the near future.
wolfgang wieland: And what is nice about this different viewpoints, is that they really bring together.
wolfgang wieland: Different totally different communities and open up a way to think about common problems in different realizations of quantum gravity and.
wolfgang wieland: This is very exciting Now the question is, or the task is to understand how gravity coppers to boundaries now, this is a bit of a maybe not a very clear terminology, but the idea is to.
wolfgang wieland: describe simply boundaries in in the gravitation and framework, but these boundaries are themselves not material systems, so they are not like wires or mirrors their dad just.
wolfgang wieland: Many folks that we introduce to isolate.
wolfgang wieland: gravitation subsystems and that requires to introduce some sort of boundary but this boundary has no material.
wolfgang wieland: presence, so to say, I mean that if we think that way, it is actually.
wolfgang wieland: quite natural to formulate gravity as a theory theory formulated in terms of differential forms, rather than tenses so to work with frame fields and connections, rather than metric variables, the reason for that is that in the.
wolfgang wieland: In in terms of differential forms, there is a more primitive notion of.
wolfgang wieland: Of projection, namely the pullback which does not require any metric structure so it's more more.
wolfgang wieland: yeah it's a more primitive notion of defining what is intrinsic to a boundary.
wolfgang wieland: And if we formulate gravity in terms of differential forms, this is all very.
wolfgang wieland: familiar to us, then the configuration variables are the ultimate frame the diagonal license the metric and the notion of parallel transport, then the action is just the usual Palestinian action, which is the field field strength of the connection contracted with directed area.
wolfgang wieland: To form so five extra value to phone, which is the urbanski to form to impose boundary conditions and make the action.
wolfgang wieland: Different variation of principle well defined, we may need to impose additional boundary terms.
wolfgang wieland: That then show up as corner terms in the simplistic potential complexity potential for the polar teeny action just tells us that the connection is economically conjugate to this to fall at the kinematic level.
wolfgang wieland: And then, what, what are the charges engage cemeteries in well, since we are now working.
wolfgang wieland: With frame fields, rather than.
wolfgang wieland: metrics variables, we have one additional gauge symmetry, namely internal Lawrence transformations that act by rotation on this tensor indices, and the.
wolfgang wieland: Lawrence connection.
wolfgang wieland: it's been connection transforms accordingly by a degree of it, and what one then finds is that there are additional launch charges that are.
wolfgang wieland: generators of the H symmetry so more.
wolfgang wieland: More precisely, any swore such launch transformation is indeed a gauge cemetery, which means that it is the general direction of the.
wolfgang wieland: Press and elected to form on share, but a large cage transformation, so a large such internal lauren's transformation is not against transformation, it is actually a physical server that is generated by this.
wolfgang wieland: observer, which is the electric flux through the boundary.
wolfgang wieland: And in fact this quantity, has also been studied previously or long time ago by people interested in defining class a local spin off the gravitational field, for instance, I think your name.
wolfgang wieland: On such references Branson who introduced such fluxus as the notion of the internal spin or angular momentum of space time and that already hinted an important point, namely that, without any.
wolfgang wieland: Community group degrees of freedom, it is kind of.
wolfgang wieland: unnatural or not not back here what is there a physical significance of these charges and.
wolfgang wieland: In from out from the perspective of our.
wolfgang wieland: Community has been some recent interest in this.
wolfgang wieland: In these charges by Mark and and I adore and.
Many other and the people I must say and.
wolfgang wieland: More importantly, because the, these are the charges, corresponding to.
wolfgang wieland: To angular momentum linear momentum Center of mass of course the different offices that act on the fundamental fields on the fundamental configuration variables by the derivative Mathematically speaking it's actually the derivative lifted upwards into the Lawrence on which says that.
wolfgang wieland: A leader narrative of the connection is basically the.
wolfgang wieland: field strength contracted with.
wolfgang wieland: With the vector field that generates different models and then and now you can ask an important question so in saying in in general relativity if you move isms are gauged symmetries but the lesson from any gauge theory is that.
wolfgang wieland: gage symmetries have charges and sort of question is, what are the charges for these different systems and if you're not take this inflected to phone and ask whether it is hamiltonian whether it is a charge.
wolfgang wieland: That generates these different systems, then the question boils down to whether this expression has his differentiator, but it has a general.
wolfgang wieland: And in fact at the linear is lever, this is truly fulfilled, because this action becomes linear and, once it is linear you can truly integrated and indeed you find the charge and you also find that once you evaluate this charge it space like infinity for an astral particular flat.
wolfgang wieland: Space time where perturbation is points off like one of them are then indeed you obtain the usual conquer a charges, you have a pain, for instance, if sigh is an awesome topic and translation that Piques I is just a mass.
wolfgang wieland: So now, this sounds very.
wolfgang wieland: neat and.
wolfgang wieland: interesting, but now passes a piece appears and what and the person that appears is that that that the side of interaction of gravity with itself actually spines the integral ability that for Agenda, or more precisely for.
wolfgang wieland: If you asked for that such an.
wolfgang wieland: generator exists for finite region, then you find that there isn't not any longer such charge existing so let me go a bit through this argument because it's very simple.
wolfgang wieland: So in gravity, we know that if you malfeasance our pH symmetries small differential isms of each cemeteries and therefore we.
wolfgang wieland: may assume that, if we restrict the hamiltonian formulation to a finite region that then to we can assign a generator to such a time, translation and if we.
wolfgang wieland: take into account water but i've said previously.
wolfgang wieland: We were you find that this generator can only be surface charge.
wolfgang wieland: boundary term you can ask.
wolfgang wieland: Well, is there now, you can run.
wolfgang wieland: audit, the question is better something like Robert it's true, and if it is true, then you would say that this hamiltonian that generates the evolution along the boundary.
wolfgang wieland: has actually is actually Mediterranean and that there is some stress energy pencil for some boundary field theory that generates this evolution, but now we can ask is this actually is best is actually.
wolfgang wieland: Under which conditions can this be true.
wolfgang wieland: And when we also know that any such generator must fulfill since the underlying symmetry is if your mouth is symmetry that we should have some.
wolfgang wieland: representation of.
wolfgang wieland: dpm off isn't symmetry algebra on Facebook.
wolfgang wieland: Perhaps with us, yes.
Abhay Vasant Ashtekar: Oh very base level what what what Facebook of.
wolfgang wieland: i'm talking about the covariance a space yes.
Okay.
Abhay Vasant Ashtekar: But then the simplistic structures, has a lot of digital resources so that we are taking that into account also.
Abhay Vasant Ashtekar: Inspired Facebook doesn't have a I mean the gauge directions, are all in the current political structure.
wolfgang wieland: that's right yes.
Abhay Vasant Ashtekar: So, so you have to worry about the degeneracy is also in this thing that us, I mean the hamiltonian.
Abhay Vasant Ashtekar: Yes.
wolfgang wieland: Yes.
wolfgang wieland: Yes, that's correct and what what so in this kind of.
wolfgang wieland: motivation and argument in here and here.
wolfgang wieland: The question is what.
wolfgang wieland: What what face face can be assigned to to find that region, so if I separate the degrees of freedom on to such a cushy partially cushy hyperspace.
wolfgang wieland: And then indeed the JET then, then the simplex extract pressing likely to form on the cover and face space has huge too generous as you're saying, in fact, any small give you more of isn't.
wolfgang wieland: That is of compact support on this on this partially cushy hyper surface is the general direction.
wolfgang wieland: But for find it from officer, which is to say a few more isn't that doesn't vanish or which is generated by vector field that doesn't Jana doesn't vanish you at the boundary you find that this is not a.
wolfgang wieland: gauge cemetery so you can ask yourself, is there is there hamiltonian for such a.
wolfgang wieland: For such a few more ISM and is that and this hamiltonian can only be a charge, it can only be a surface and deliver over the boundary but then you also let us also assume that.
wolfgang wieland: That different office manager Brian satisfied, so that you get that the add on the covariance face space.
wolfgang wieland: If you find that persona brackets that these generators satisfy some algebra perhaps with some central charge, but now this viewpoint, is it ought, it is at odds with the fact that a system may lose energy by a gravitational radiation.
wolfgang wieland: And the argument.
wolfgang wieland: They have a realistic argument is as follows, so let's assume that this generator actually is energy.
wolfgang wieland: Energy, as mentioned, for instance, at an infinity but now brought brought into final distance, then we can ask what it is, what is it was what is its time evolution well time evolution is generated by.
wolfgang wieland: By a vector field and we just.
wolfgang wieland: assume that there that this vector field is integral rubber on combined face space, such that we can use it's generated so replace God T by the hamiltonian but then whatever appears in here, in this first line is.
wolfgang wieland: Because the lead the derivative of a vector field with its have manages this just this must be conserved.
wolfgang wieland: But this is a at odds with the very simple observation that energy is predicted the rain.
wolfgang wieland: And if if we think of discharge being located at infinity then indeed it should just be that the mass of the system and the energy loss should be just.
wolfgang wieland: The bondi you should be just getting by the body mass forward and therefore these two equations are at odds with this viewpoint there's something wrong about this viewpoint, and I think one.
Abhay Vasant Ashtekar: And now there's nothing wrong with that the point, because if you just take four Sigma with your.
Abhay Vasant Ashtekar: Real coaches surface, which is the past one.
Abhay Vasant Ashtekar: Then, and that is that there's a total energy and that energy is concert.
Abhay Vasant Ashtekar: Right, so I think if you, the problem is that you are.
Abhay Vasant Ashtekar: Having the cake and eating it dude you're trying to say that.
Abhay Vasant Ashtekar: The Sigma can be anything any cross section.
Abhay Vasant Ashtekar: And still, it should be the hamiltonian and then it doesn't come up with itself, I mean.
Abhay Vasant Ashtekar: In other words, your your your first equation, the slide.
Abhay Vasant Ashtekar: If you stick stick to anything you want that, of course, is incorrect, but if you take Sigma to be the kosher surface for that little region, then it is correct.
wolfgang wieland: That is correct, of course, there is nothing wrong about it, and then you don't get this is this maslow's formula, because you always located at and I not at.
Abhay Vasant Ashtekar: No, no, no, you get mass loss by the law because.
Abhay Vasant Ashtekar: Because I mean what you get conservation law which says that the the bottom integral is equal to the integral through the through the null surface, plus the top integrity and that is a conservation law.
Abhay Vasant Ashtekar: And then the bondi energy, if you like, the local version of the body energy would be the one that is evaluated the top service and I just don't understand, we were noticing, so why are we discussing.
wolfgang wieland: So we are these.
Be because I.
wolfgang wieland: want I want precisely a framework that is MOD.
wolfgang wieland: That allows me to to study an arbitrary cushy hyperspace to to to study us to study.
wolfgang wieland: A tree surface that that is not cushy that ends up that can intersect a cross section at it's quite Plus, for instance, and this is.
wolfgang wieland: And to clarify this is also the same viewpoint that appears on an isolate that reason because there we have.
wolfgang wieland: We have we have a similar setup there as well.
wolfgang wieland: The separate degrees of freedom inside the black hole or inside the isolated horizon from those that sit outside, so we are in a in a framework where we are considering partially cushy hyper surface three surface that intersects an isolated horizon and we asked is the hamiltonian that.
wolfgang wieland: generates evolution along that.
wolfgang wieland: That brings us from one cross section to the next.
Abhay Vasant Ashtekar: I said I mean, for example, you know long time ago, many years ago, before even the work of war that was in the.
Abhay Vasant Ashtekar: In the in the chat bar just now Bob Bailey.
Abhay Vasant Ashtekar: Royal line I have done this course, you have this formulation exactly for the bottom, being a Porsche surface the top being a cross section of scribe and we showed that there is.
Abhay Vasant Ashtekar: it's completely consistent Korean face face.
Abhay Vasant Ashtekar: In fact, you get the bond the last last last formula right.
Abhay Vasant Ashtekar: We mean.
wolfgang wieland: The question is, for this down the line.
Abhay Vasant Ashtekar: Which is.
Abhay Vasant Ashtekar: The the the time translation of activity.
Abhay Vasant Ashtekar: Is the.
wolfgang wieland: One, the question is what is.
wolfgang wieland: What is the role of.
wolfgang wieland: Of Sigma on that Facebook, so what was.
Abhay Vasant Ashtekar: You sick sick sick that the future Sigma.
wolfgang wieland: And then sort of flux.
wolfgang wieland: Some or not let's say.
wolfgang wieland: And what i'm but maybe this will become clear in the in the next slide what i'm what I want to argue for is that.
wolfgang wieland: We can indeed.
wolfgang wieland: Think of hamiltonian framework where we can put any flux it crosses the narrow hyper surface, but then we have to treat it differently if you have to view it as some.
wolfgang wieland: Not part of, then we have to work on as smaller facebook's, we have to work on this pace pace, but the outgoing flux, is just PICs.
wolfgang wieland: So it's not it's not a cue number, so to say it's not a face space number, it is a, it is a background fee, and then the question is, are there is there still a space that evolves for that given background fields.
wolfgang wieland: And that's what I would like to to other that's the viewpoint, I would like to to advocate for that we can have a hamiltonian that brings us from one.
wolfgang wieland: Such cross section to the next, but it operates on a base smaller pace pace in fact it operates on a pace space that is only the face space of these boundary modes alone we're already at theta has now been.
wolfgang wieland: encoded into into this out silly repeats.
wolfgang wieland: and
Abhay Vasant Ashtekar: Bad but you're not forced.
Abhay Vasant Ashtekar: To that is what i'm saying I mean that's I mean.
wolfgang wieland: that's another famous precisely precisely i'm.
Abhay Vasant Ashtekar: So, so that we can just say let's make that choice because the way that he was presenting it, is that there is some contradiction if you are going to go away and face space in that space time reason i'm saying there's no contradiction.
wolfgang wieland: Right, there is no, there is a contradiction a few, if you want, in a way too much, and you, but you can have that if you if you drop another um.
wolfgang wieland: If you abandoned and another.
wolfgang wieland: If you treat certain kind of variables differently.
wolfgang wieland: So I think we are, we are not.
Abhay Vasant Ashtekar: Okay, good.
wolfgang wieland: yeah let me, let me go ahead.
wolfgang wieland: So let let's.
wolfgang wieland: was, in my opinion, what lies at the.
wolfgang wieland: At the heart of the problem is, is that in the combined face based approach we we don't.
wolfgang wieland: It is somewhat different difficult or not immediate two separate faith based degrees of freedom from backgrounds feeds or put in other ways to separate Q numbers from.
wolfgang wieland: From see numbers or pete configurations from from p's and q's on face bates, and this can be illustrated so this program can be illustrated by the following extremely simple time model so consider.
wolfgang wieland: A large system, so a system and its environment, and it is completely hamiltonian so all the degrees of freedom are just encoded in some p's and q's that evolve a court, according to a large hamiltonian.
wolfgang wieland: But now let's suppose that we are only interested in in a subsystem and the subsystem is governed by the following action it has some p's and q's so face face.
wolfgang wieland: can only two potential minus syntactic structure some pre hamiltonian and, in addition to that, and interaction term that tells us how the system degrees of freedom interact with the environment, now.
wolfgang wieland: The whole system system and the environment if or by a large hamiltonian but if be separate the system from the Environment some degrees of freedom, have to be prescribed by the external.
wolfgang wieland: system and I encode them into these fields on the guy of tea, which are called background fields.
wolfgang wieland: You can think of them as for instance the length of.
wolfgang wieland: pendulum or the strength of a harmonic oscillator whatever in the large face face all these degrees of freedom are hamiltonian, but if you separate them.
wolfgang wieland: be prescribed some degrees of freedom as external variables these external variables can be tuned by the experimenter.
wolfgang wieland: By by turning some notes and drops, and so there is an explicit time dependents now what his face face face face in this prescription is just our p's and q's that.
wolfgang wieland: satisfy the hamiltonian equations for given back France fields Omega I have T, however, the space of the six weeks is larger than that it contains all possible configurations of omega of T.
wolfgang wieland: So the space of physically histories, is the Union the discharge Union of all face basis for all possible configurations of omega of tea.
wolfgang wieland: And now in in this time model, everything is kind of obvious we know what his face face, we know bodies, the hamiltonian and we know what our back from fields.
wolfgang wieland: In general relativity, on the other hand, behind the situation where this separation is not immediate, in fact, it is sometimes we sometimes don't know the hamiltonian at just at hand.
wolfgang wieland: And the combined faith based approach is a very elegant way to infer the hamiltonian from the from the action.
wolfgang wieland: However, they cover and paste This approach does not directly operate on tastebuds it operates under space of our solutions to the field, the patients to our possible boundary conditions.
wolfgang wieland: instance in and with better say compatible with an awesome particularly flats based on but, in doing so, but if he if he can then do the same.
wolfgang wieland: If he then apply the same viewpoint today that program we run into the following issue in, so let us so we know that what is the hamiltonian in this framework it's just a free hamiltonian plus this interaction term and now consider a general variation on.
wolfgang wieland: On face to face, in other words at on this excuse me, I said something wrong let's consider a general variation in other words a tangent vector.
wolfgang wieland: On the space of physical histories, a tangent backdrop on this space of physical histories, is an infinitesimal variation of the p's and q's and omega and now the variation of the hamiltonian which we know because it's just a pre hamiltonian plus the interaction hamiltonian is.
wolfgang wieland: contains two terms it contains a simplistic term that takes care of the dependence of the hamiltonian with respect to the p's and q's but it contains an additional term that.
wolfgang wieland: takes into account the dependence of the hamiltonian on the background fields, and so one may not be mistaken to believe that the hamiltonian is not integral over.
wolfgang wieland: Because there's always this additional term but this non integral ability, just to reflect the pack the simple fact that the hamiltonian is explicitly time dependence that the explicit time dependence is.
wolfgang wieland: Is induced by this explicitly time dependent extra fields, in fact, if this top Now you can evaluate this equation, for a very particular.
wolfgang wieland: tangent vector on the space of physical histories, namely that time evolution itself, then the first term vanishes but the section term gives you something, namely gives you the time dependence of the hamiltonian.
wolfgang wieland: They explain it so if, in other words, if you replace he a delta idea with et system those have a and your pain, the equation, the governance, the time dependence of the hamiltonian and this equation just assume that the time the pendants is driven by this time dependent veterans.
wolfgang wieland: And now the the viewpoint is to ask how that this can be applied to to gravity so.
Excuse me.
wolfgang wieland: So the what we have to ask ourselves ourselves now is how to how to separate the environment from them.
wolfgang wieland: From the system to be started and in the current context to characterize gravitation is subsystem two choices must be made.
wolfgang wieland: first choice is is is one could say top logic, so you start out with the partial cushy hyper surface Sigma and now you have to.
wolfgang wieland: To give a prescription for how to extend this.
wolfgang wieland: This partially cushy hyper surface into a virtue in space time into a region of space and the infinitely many possibilities for how to do that.
wolfgang wieland: And, for instance, you can say that this hyper surface should be time like or minimal surface extremely surface or this surface of consuming curvature etc in following the are interested in the case where the surface is not.
wolfgang wieland: In addition to this first choice is first choice which is topological a second choice must be made, namely, what are the degrees of freedom that live on this on this.
wolfgang wieland: Narrow hyper surface, in other words, what are, what is the flux of gravitational radiation that goes out, and if you have these two choices, you can.
wolfgang wieland: evolve these degrees of freedom or you can evolve you, you find a hamiltonian that evolves the boundary data along the cylinder.
wolfgang wieland: The question of course is the hamiltonian for which face, please, what are the degrees of freedom that invoice under this Hamilton.
wolfgang wieland: And the hint is given by our what we know from Laura mentions in fact in dimensions smaller than four there are no reputation and base to begin, so we can completely forget about that program yet.
wolfgang wieland: We still find charges, we still find a boundary filtering, in fact, if we separate degrees of freedom in the outside, from the degrees of freedom in the inside.
wolfgang wieland: For instance, if you work with in the transactions formulation of gravity you'll find some confirm or you can choose boundary conditions, such that you end up with a consumer field TV at the boundary that evolves.
wolfgang wieland: The remaining degrees of freedom along this along this boundary for which you have to give you a prescription how this boundary is embedded into space time.
wolfgang wieland: And what are these these degrees of freedom that live at the boundary well, they cannot be happy tones because in order mentioned Stan or cartoons, to begin with, they are just this.
wolfgang wieland: boundary degrees of freedom or these animals that lift that are only located at the Cross sections at the corners of these space time regions and the question is whether something similar can be done in higher dimensions and.
wolfgang wieland: You pointed out, I like to advocate in this talk.
Abhay Vasant Ashtekar: Is.
wolfgang wieland: that yes, this can be done, but then this hamiltonian that generates this evolution is.
wolfgang wieland: It depends parametric Kelly on the in or outgoing flux and that then drives the explicit time dependence of the hamiltonian.
wolfgang wieland: So, and now the question is how to to set the.
Stage question.
wolfgang wieland: So now, the question is how how to set up the problem.
Abhay Vasant Ashtekar: How to.
wolfgang wieland: choose the surfaces.
wolfgang wieland: Now, in other words, am interested in setting up a debris knife radiation or to choose surfaces in space time that abandoned by not hyper surfaces and then take the limit.
wolfgang wieland: To to infinity in order to see better this framework is consistent with what we have introduced or what we have learned so far by by all the previous work so.
wolfgang wieland: most commonly in the literature, the following gauge choices are being made.
wolfgang wieland: So these are the, these are the standard Newman panels or this is john standard bondi coordinate system, so one works with.
wolfgang wieland: Not affiliation, but now the outgoing not hyper surfaces I integral over and the human painters not Tetra introduced which is parallel Lee transported along these outgoing non directions.
wolfgang wieland: The retarded time coordinate you select this ubiquity constant blue hyper surfaces, which are not.
wolfgang wieland: In addition.
wolfgang wieland: They are they going now directions which are, however, not surface orthogonal.
wolfgang wieland: Instead, a there are other it constant hyper surfaces, which are usually timeline.
wolfgang wieland: And this.
wolfgang wieland: cage choice is somewhat is advanced disadvantages for our purpose, because we want to assign a face space, so we want to characterize the outgoing no direction at at not hyper surfaces that can record this radiation and therefore we want to have the blue that excuse me that read.
wolfgang wieland: This read surfaces to be non surfaces as well, so, in other words, we want to work with the debris not affiliation, of course, this will at some point, this coordinate system will at some point break down so we.
wolfgang wieland: So what i'm doing in the paper is to restrict myself to.
wolfgang wieland: To region where this.
wolfgang wieland: person exists, basically, and now the idea is that the the radio coordinate is simply.
wolfgang wieland: replaced by the inverse conform or factor and still days to retarded time coordinate who's youthful constant surfaces again So these are the outgoing knowledge surfaces, but both of these.
wolfgang wieland: But now we have a doctrinal foundation now one of the coordinators, you and the other one is the inverse conformed factor.
wolfgang wieland: and in doing so, some spin coefficients that have been previously said to CEO and i'll turned on.
wolfgang wieland: And therefore we have to relax some other gauge choices which can now not any longer be imposed in the standard Newman and rose.
wolfgang wieland: On the communism, in fact, what is what what is no no longer true is that the not attach what is purely transported along the outgoing i'm surfaces, so this condition is.
wolfgang wieland: abandoned.
wolfgang wieland: Instead, that in going now direction is now surface orthogonal so there's a gradient and this gradient so in going that direction is proportional to the gradient of all.
wolfgang wieland: The only received room of the.
wolfgang wieland: Previous page condition that says that the earliest age condition that says that is not Tetra is power really transported along the outgoing directions, is this you want beach condition basically sets select representative of the.
wolfgang wieland: Extra fields M and N bar that are.
wolfgang wieland: tangential to these 2d cross sections where they're going and outgoing non directional.
wolfgang wieland: intersect and this such a dominant affiliation, is now more advantageous for purpose, because for every hole so for every value of the inverse conform or factor.
wolfgang wieland: We now have such a region and we can ask what is the syntactic structure that we induce, for instance on the nikon but also on these casts on this partially cushy harper surfaces as inherited from the action from the action that we define in one such region.
wolfgang wieland: By imposing appropriate boundary conditions, what is now Nice is that using this.
wolfgang wieland: w not affiliation you end up basically with exactly the same full of conditions, as in the Newman Penrose in the as in the bondi gauge the only difference is that some spin coefficients that are otherwise set to zero have now.
wolfgang wieland: known vanishing a non vanishing value but order so to St martin's been coefficients life, the expansion in going into their.
wolfgang wieland: outgoing and ongoing expansion outgoing and in going cheer you don't have the same.
wolfgang wieland: phone off as.
Abhay Vasant Ashtekar: Just just to make sure that your rotation is opposite of newer Penrose like for you.
Abhay Vasant Ashtekar: What what you call K, is what they call.
Abhay Vasant Ashtekar: The what you call what they call it.
wolfgang wieland: Yes, that is correct.
wolfgang wieland: Yes, but it's.
wolfgang wieland: Closer to work on the original us.
Abhay Vasant Ashtekar: that's perfectly fine, but so that.
Abhay Vasant Ashtekar: Other people don't get confused about it so.
Abhay Vasant Ashtekar: When you say Sigma some key, that is what Newman Penrose what's called the sheer, and that is sequence of Allah and what you call Sigma suppan Allah is really what they're called segments of N, which is war, like the news OK.
wolfgang wieland: that's fine, yes, you see, you can infer from this time derivative in here.
Abhay Vasant Ashtekar: and said that that Sigma you didn't like what that was it okay yeah good good Thank you yeah.
wolfgang wieland: And, and also to speak there for for.
wolfgang wieland: Various.
wolfgang wieland: curvature.
wolfgang wieland: The components of the buyers tend to have the same four of us in the standard numerous formulas which is my Nice and.
wolfgang wieland: So this sets up the fall off for one particular.
wolfgang wieland: solution of einstein's equation in this coordinate system this doesn't tell us yet about anything about Facebook Facebook is not about one.
wolfgang wieland: Space time it's about.
wolfgang wieland: Family of solutions of space time for given boundary conditions and the via in the following i'm studying the solutions of einstein's equations in in a finite region, in fact, in one of these.
wolfgang wieland: Regions defined by this coordinate.
wolfgang wieland: And the question is now how to set up the.
wolfgang wieland: original principal how to set up the action, what is the what is the free space and so on.
wolfgang wieland: And now, now we go back to.
To.
wolfgang wieland: To the face based formulation.
wolfgang wieland: And to set up the boundary conditions, it is useful to study the structure of.
wolfgang wieland: The fundamental configuration variables on this on and our hypothesis now in our approach in Luke quantum gravity that momentum conjugate to the connection is terrible urbanski to fall.
wolfgang wieland: So we have to study how this this if you decompose it into it served well and antisense two parts, how this parameter prizes or how this just looks on the null hypothesis.
wolfgang wieland: And what is nice is and i've no i've spoken about that already many times is that the poor back of the pound key to form to dinner surface has a very simple algebraic structure, it is in fact now these fields are intrinsic to the north boundary the symmetry 10s of product of a spinner.
wolfgang wieland: which I call l.
wolfgang wieland: For the same reason, I call the knowledge generators L and SP no value to fall.
wolfgang wieland: And the role of this spinner la is, it is just a national flag to the associated to this new direction so, in other words, if we take a bar.
wolfgang wieland: In the Newman Penrose formalism this corresponds to another vector and this novel vector is tangential to the nine race that generate is not a surface furthermore be can construct so all these fields are now charged on very sad to see.
wolfgang wieland: But since days the SL to see invariant epsilon tensor we can contract these to spin out spinner indices, and we get something that.
wolfgang wieland: defines is kayla and I said to see, so this is the geometrics kayla it lives on this not hyper surfaces, and it has a geometric meaning, it is simply the area area to form the oriented area on this.
wolfgang wieland: On this not hyper surface I say oriented area, because this can be both positive and negative corresponding to a different choice of orientation, while the metrical area is always.
wolfgang wieland: Positive so it's the difference between the density and the and the differential for.
wolfgang wieland: And now, what is the.
wolfgang wieland: Now we.
wolfgang wieland: Are additional principle, so we have to actually in the interior and the bark in the inside, these.
wolfgang wieland: These cones but now we have to add a boundary term on this night hyper services is red.
wolfgang wieland: regions.
wolfgang wieland: And what is nice is that from these boundary fields, one can construct about there is an obvious choice for boundary term, which is just the derivative of the spinner contracted with to form eater.
wolfgang wieland: And one has to add, however, an additional one form that is pounder that is intrinsic to the boundary which encodes them.
wolfgang wieland: The rescaling freedom, you have in the novel directions, and this is a connection that is intrinsic to the normal hyper surface now, the question then arises, what should we choose for this.
wolfgang wieland: One form, and this will be chosen by the boundary conditions that I will specify the next slide now the words on the not hyper surface, we have to impose.
wolfgang wieland: So the combined action is now the some of the action in the interior plus this boundary and now we have to now, I have to tell you what are the boundary conditions under which does action is to be.
wolfgang wieland: Extra month and on the the boundary conditions are as follows, in fact, basic idea is that along the not hyper surface the boundary conditions should only fix two degrees of freedom point which is of course the gravity.
wolfgang wieland: gravity monster.
wolfgang wieland: This just the gravitational radiation, it needs to be fixed but we don't want to eat any more of that and the way to do that is to say that and get equivalence class of boundary fields is kept fixed at the boundary.
wolfgang wieland: How is this.
wolfgang wieland: And this case, your equivalent class is defined by an equivalence relation, so any there the equivalence class or the boundary fields consists of the knowledge generators and I keep the.
wolfgang wieland: The direction of the novel race fixed So these are seen as an as a university strong structure shared among different space times so bodies shared is the direction of L but not it's not it's.
wolfgang wieland: A feature length, so to say.
wolfgang wieland: In addition.
wolfgang wieland: there's the one from copper that defines the non affinity and then these diets em and then bar that defined intrinsic metric on the 900.
wolfgang wieland: And now we have to induce or now, I have to say that I have to specify this equivalence relation and to configurations are said trivalent if they are related by a different, more isn't it is vertical not worth it from office, and that is generated by.
wolfgang wieland: baxter field that is not on the novel hyper surfers then that the locations.
wolfgang wieland: Complex unified.
wolfgang wieland: and former transformations and shifts of this one from CAFE the basically is basically tells you that the only component that matters of copper a of that one form is the one that defines the non affinity acceleration which and then you can easily if you do the accounting.
Then.
wolfgang wieland: You learn that this this.
wolfgang wieland: Equivalence class is characterized by two degrees of freedom point which are the two degrees of freedom of gravitational radiation crossing the non episodes.
wolfgang wieland: Now.
wolfgang wieland: An interesting question, and this is going into the direction that i'm.
wolfgang wieland: Working on now is how the mercy parameter affects the structure and also changes the boundary conditions in fact in there.
wolfgang wieland: In terms of sex to a variable is it's very easy to introduce the mercy parameter just replace you just add a complex value coupling constant to the self to an action and take the real power of of the entire expression and that defines the party or host action.
wolfgang wieland: And on the boundary you just do exactly the same you just multiply the you just add is complex value coupling constant in front of your boundary action.
wolfgang wieland: And the only book now happens is that.
wolfgang wieland: This one form that you need to add, in order to make that the boundary term involvement on the order or Kabbalah and under and the locations now changes its.
wolfgang wieland: Its meaning or its changes its geometric significance, the boundary conditions of formerly the same However, their definition of these equivalents relation this equivalence class is now.
wolfgang wieland: changed or affected by the introduction of of the mercy, what do you find in fact is that.
wolfgang wieland: Is one form CAFE is now the you want analog of the Su to Africa avail connection in fact it's time or it's not a component is a combination of.
wolfgang wieland: The Non affinity of united direction plus one upon gamma.
wolfgang wieland: available in mercy parameter times.
wolfgang wieland: against potential, which is the you want, on a lot of the spin connection so can be.
wolfgang wieland: obtained from the derivative of your knowledge like long the non directions and what do you then.
wolfgang wieland: have to do is that or what do you then find this that this one from CAFE behaves as a connection both thunder Bay locations and you want gates transformations, and that makes it them know surface on a log of that is Jacob ever connection.
wolfgang wieland: And I will expand more on that on in in the future.
wolfgang wieland: So the very near future.
should be out soon.
wolfgang wieland: And this also relates, I mean this is, I just edit to make a bit to make a bit relation to this reason papers of law and amelia mouth more explicit where etc plays a major role now so far is the group of.
wolfgang wieland: Preserving.
wolfgang wieland: linear transformations in two dimensions and how.
wolfgang wieland: How how and the relation to their faith based variables that i've introduced on the last last couple of slides is very easy, in fact.
wolfgang wieland: Out of the sheer and this you want connection, you can just construct and SL to our, so to speak, alone me alone denial generators where these generators satisfy the standard as into our conversation relations.
wolfgang wieland: But.
wolfgang wieland: That is kind of a excursion to the future, I should also finish what I told told you about the pace pace.
wolfgang wieland: So so far i've only.
wolfgang wieland: So let us briefly recap, so I introduced this debris in our affiliation, then I specified the bark corresponding the action but also specified the boundary conditions now what is missing is to derive from all that the faceplates and now.
wolfgang wieland: Yes, so at that point we're still in the covariance faceplates approach, so we only introduce.
wolfgang wieland: Some galactic potentials on an on field space, this does not get so depressed and galactic potential Peter an on field space, this does not yet define the facebook's.
wolfgang wieland: However, it defines.
wolfgang wieland: The starting point from which we can construct the face.
wolfgang wieland: On the not hyper surface we get this expression which contains sheer and expansion now, since we know.
wolfgang wieland: Since I have now introduced this topic in our affiliation, I can take the limit to infinity so where this remember this red.
wolfgang wieland: Top navigation and now I can just take this given volume to infinity and evaluate the syntactic structure and what you then obtain is indeed just the usual.
wolfgang wieland: radiative.
wolfgang wieland: pace pace as as as it was introduced by by.
wolfgang wieland: Many years ago, and this is very nice, because it is, it is a consistency check it tells you that.
wolfgang wieland: From this.
wolfgang wieland: domino affiliation, you can.
wolfgang wieland: recover the face face value infinity in the same way, you can also go to a different types of.
wolfgang wieland: insight and the manifold, namely an isolated horizon for instance where the sheer vanishes and so does the expansion so you're just left with.
wolfgang wieland: With with this term, which is tenders electric potential and has been introduced for an isolated wise.
wolfgang wieland: But now, since then, this tabernacle affiliation or these regions that i've chosen split into have different kind of boundaries, we also mainly space like and and now we also have a subjective potential for the NRA.
wolfgang wieland: For the space like hyper surfaces, which consists of the user shirt but turning the bikes to tell us that the Africa connection.
wolfgang wieland: The sexual connection at the present like to collaborate is canonical conjugate to the flux, but this is now, this is now gets an additional corner term that tells us that the spinner valued fields are Comically conjugate.
wolfgang wieland: And let me skip this slide and I will conclude here.
wolfgang wieland: Because now i'm going back to the original form, now i'm asking is there me he said how many tonia on that face space for vector field that last tangential to this to this generates.
wolfgang wieland: And if now delta is variation on field spits.
wolfgang wieland: So, again on this.
wolfgang wieland: The at the level of this equation, we are not yet speaking about base base, this is an equation, that is true, on the fee on on combined face bits.
wolfgang wieland: Which is larger than it is not truly have a space, yet, because it has the general directions and there's and we don't really distinguish boundary fields, from.
wolfgang wieland: Faith based variables, what do you then find is that on that face based on that space, the following equation is satisfied, namely the.
wolfgang wieland: The exists hamiltonian which is integral theory, if you add this additional corner term, which is the contraction of the nars simplistic current with the normal vector field evaluated against these people.
wolfgang wieland: And the point that I like to make is that this equation is is the analogy of what I have introduced earlier, the simple time model, where we have.
wolfgang wieland: There were the hemi where the.
wolfgang wieland: The variation delta is not a tangent based on pace pace, but attention vector that.
wolfgang wieland: contains also variations of the spectrum fields and, in other words the hamiltonian depends not only on bass bass very rigorous and its dependence is encoded by simplistic potential contracted with the time direction, but it also contains a functional dependence on this.
wolfgang wieland: Additional background fields that drives the time evolution, the time dependence of the hamiltonian and if Delta, is it saves and govt, then the only term that survives is is this last term it drives the time dependence of the hamiltonian and the same is true at the level of.
wolfgang wieland: This at the theoretical level if in fact delta is itself.
wolfgang wieland: In.
wolfgang wieland: Parallel to.
wolfgang wieland: Is the Leader rooted in the direction of sight, then the electric term vanishes the second term just gives you the flux, which determines the time dependence of the of the hamiltonian and which is always positive.
wolfgang wieland: And what I have included here in this last line is.
wolfgang wieland: To to explain what is the.
wolfgang wieland: Physical significance of this coming.
wolfgang wieland: In fact, it is not directly the mass as measured by on the energy.
wolfgang wieland: But the difference differs from the bondi energy by a term that is the area.
wolfgang wieland: multiplied with the non affinity of this direction, I think.
wolfgang wieland: And just one more.
wolfgang wieland: comment in evaluating this term.
wolfgang wieland: You have to take a limit to infinity are very close to infinity and it first, you may 1 get the impression that this term verges However, the divergence is.
wolfgang wieland: If so, if you go all the way back to the fall of conditions of spin coefficients, then the divergence is governed by that term.
wolfgang wieland: I haven't told you what our is our is the pitches katie a two dimensional which is kayla of these two dimensional cross sections, and if you integrate, which is 10 integrated against the volume volume to form the area element on these four sections.
wolfgang wieland: And this is a topological invariant.
wolfgang wieland: Namely the La la la stick.
wolfgang wieland: Was.
wolfgang wieland: Bernie and who's variation because in this equation only teletype us.
wolfgang wieland: is constant because it's a topological environment so, in other words, this term contain this equation contains a term that is.
wolfgang wieland: It looks as if it is that appears to be ub I are divergent linear in our However, the term is evaluated against the variation of a topological variant.
wolfgang wieland: vanishes because is the variation of a number of initiatives.
and
wolfgang wieland: So that's a kind of a technical remote call this limit or what has to be taken into account to evaluate these limits and.
wolfgang wieland: So let me conclude, maybe here.
wolfgang wieland: That question is.
wolfgang wieland: A question that has appeared in the literature mateys.
wolfgang wieland: Easter hamiltonian on spy plastic bring that drives evolution along this.
wolfgang wieland: Long this non hyper surface and.
wolfgang wieland: What I would like to say is this is.
wolfgang wieland: Such a hamiltonian exist if you make certain assumptions, or if you feel restrict yourself to a.
wolfgang wieland: to certain to certain floor Leah or certain services in coburn face space, namely those were the outgoing flux is is fixed or treated differently, not as a as part of a space for treated as a.
wolfgang wieland: field.
and
And I think I can continue.
Thank you.
Jorge Pullin: But any questions.
Jonathan Engle: I have one question so you're treating the boundary variables like background fields, as you just emphasize again.
Jonathan Engle: But you said, with some collective structure for them, which really you would have for a face space so i'm wondering.
wolfgang wieland: yeah yeah yeah.
Jonathan Engle: I know that.
wolfgang wieland: I read that this may be a bit confusing, but again, this is.
wolfgang wieland: This decent decent now choices, you can make or choices that we can make, so we can say.
wolfgang wieland: I want to go to a face space where I treat their radiative data as as a faceplates Okay, you can do that, and then you have to, then I have to give you a simplistic structure and it's what i've written in that line, but you can also have a different viewpoint.
wolfgang wieland: And, which is equally legitimate, you can ask is there hamiltonian That brings me from one cross section to the next forgiven products.
wolfgang wieland: Now that is a different, this is also hamiltonian Christian but it operates on a different Facebook and now you have to ask what is the simplistic structure that you find on that face order that you.
wolfgang wieland: That you have to choose for that face face and it's given it will be good given on on that line where you now have to constrain that face space, so you have to evaluate this syntactic structure for only those configurations that are compatible, without going flux.
wolfgang wieland: And then I would say, then, then there is still a hamiltonian that generates this evolution and it's given by this this.
wolfgang wieland: This formula and, indeed, your question is precisely at the is the crucial point and.
wolfgang wieland: But i'm not trying to say one viewpoint is the correct one and the other one should be disregarded what i'm trying to say is that there are different choices and different ways to look at.
wolfgang wieland: At at at the system from a hamiltonian perspective and.
wolfgang wieland: and
That.
wolfgang wieland: And perhaps for each of them days there's a there's a quantum perspective, you know and.
wolfgang wieland: And I think that is a very.
wolfgang wieland: yeah that's a very interesting PCT question, you can ask what is the.
wolfgang wieland: What is the evolution from one cross section to the next, even the outgoing cheer and Easter Easter the quantum theory associated to these questions, normally we ask.
wolfgang wieland: We think of it in a nice matrix big picture, what is the problem, given some in going radiation here given some outgoing radiation there, what is the probability to go from here to there.
wolfgang wieland: But then you have so you can also ask different questions, we can perhaps we can ask questions of the following, so what is.
wolfgang wieland: Given a boundary State on a cross section here in the foundry straight stayed on a cross section there, what is the probability to grow from one cross section to the next, even the outgoing flux and I think that is also an interesting question and privacy this question that can be answered.
wolfgang wieland: directly, then the one which is about estimate.
Abhay Vasant Ashtekar: But so let's take your second point of view, which is to say that you're fixing the radiative degrees of freedom on the boundary, so there is not so that then drops out of the synthetic structure is that right or not.
wolfgang wieland: Yes.
Abhay Vasant Ashtekar: Okay, so, then that way but he's got to say that anyway, the hamiltonian there is a lot of freedom to add, I mean anything which is constant.
Abhay Vasant Ashtekar: Hamilton is determine all you have to constant I mean it's something we just constantly but then, why can't I just say that the how do I know that the the right answer is exactly the bondi mean, why is it not.
Abhay Vasant Ashtekar: want them.
wolfgang wieland: Right, because any functional Sigma say.
Abhay Vasant Ashtekar: yeah for any any function i'm sick right.
wolfgang wieland: Yes, that is yeah, that is true that kind of.
Abhay Vasant Ashtekar: So, so that I mean so that is a key point that you did not emphasize that this procedure will not tell you what the value of damage, because you wrote down hamiltonian something for something right.
Abhay Vasant Ashtekar: Before that you wrote down the formula we said that the hamiltonian was equal to the bondi plus some book or something like that.
wolfgang wieland: Yes, that's right.
Abhay Vasant Ashtekar: But then I mean Hamilton is unusual, I think that is a key point here I mean this undetermined up because it can be any function of Sigma.
wolfgang wieland: Any.
Abhay Vasant Ashtekar: I mean, I can add to your answer any function of Sigma.
wolfgang wieland: Yes.
Abhay Vasant Ashtekar: But isn't that doesn't add value in that it doesn't have much of a significant right, I mean I could.
Abhay Vasant Ashtekar: I could choose to say that the hamiltonian is just the corresponds to the 01 the flax or zero body energy.
Abhay Vasant Ashtekar: I mean the body energy doesn't change.
Abhay Vasant Ashtekar: I can make it that happen by by just choices deposits yeah.
wolfgang wieland: Yes, that is a fair remark, however.
Abhay Vasant Ashtekar: i've been the user yeah.
wolfgang wieland: No, but what I would say that.
wolfgang wieland: it's a necessary condition that you get what I what I.
wolfgang wieland: What I wrote down.
Abhay Vasant Ashtekar: I get it so thought up to that item vicki i'm fine with you, but I think that the key point next but, most people would be to know what is a Monday, energy or what is a body flux and in New York er.
Abhay Vasant Ashtekar: Actually, the body FLEX I mean the difference between the between the.
Abhay Vasant Ashtekar: body mass of two different cross sections and according to you, apart from the dimensional consideration, it can be any function of Sigma.
wolfgang wieland: When I would say that.
wolfgang wieland: That.
wolfgang wieland: So I I presented this in the answer to to the previous question, I presented these two viewpoints is to face basis that we can speak.
Abhay Vasant Ashtekar: No, but I want to take this you're saying that there are two viewpoints, am I can take the either.
Abhay Vasant Ashtekar: And I didn't.
wolfgang wieland: know I thought I want to say is that.
wolfgang wieland: automatically there must be a relation and I think this will this I mean the dance is not very great, but I think that that the relation will provide that.
wolfgang wieland: will make only one choice of the the hamiltonian work, in other words, you want to what what is, what do you say me Tony and in the one what is tammy Tony in one.
wolfgang wieland: viewpoint it comes flux, or the difference between two hamiltonian narrow viewpoint, so there should be a relation that them.
wolfgang wieland: yeah the difference between two hamiltonian is then we realized as the as the bondi flux in our viewpoint.
Abhay Vasant Ashtekar: So you brought the what you call the first somebody else wants to ask a question I, this is a continuation of the same point so in this finished.
Abhay Vasant Ashtekar: In broad terms what you call the first viewpoint, in which the boundary degrees of freedom are not fixed his besides my viewpoint that were taken a long time ago and I do this with this point paper with the.
Abhay Vasant Ashtekar: Royal line belly.
Abhay Vasant Ashtekar: And then we got the usual bonnie formula.
Abhay Vasant Ashtekar: But then.
Abhay Vasant Ashtekar: i'm kinda answer, or what am I learning by taking the second point of view.
Abhay Vasant Ashtekar: We know the answers we know everything, so what am I learning by saying that well I could also consider another face space and with a boundary Dickies of.
Abhay Vasant Ashtekar: frozen what new information, am I getting from that second viewpoint.
wolfgang wieland: I think what do you get is.
wolfgang wieland: Any and and you have a new perspective on what for holography can do and can not do so, I would say hello, or if he cannot characterized radiative or cannot capture the radiative degrees of freedom, it is a theory only of these today is called I mentioned to.
wolfgang wieland: edge degrees of freedom and.
Abhay Vasant Ashtekar: Maybe that you just.
Abhay Vasant Ashtekar: keep on you should have emphasized right I this I agree with, so that one could just say that well door point up here is just that right that holographic cannot do that and then.
Abhay Vasant Ashtekar: And then you know the other things are consistency checks, namely that one can go from one viewpoint on other and as you're saying, but consistency, then you would get the.
Abhay Vasant Ashtekar: usual answers but holographic cannot do this is the main point right and because everything else will not be for the first few pointers known before it is a second view point that you are introducing new.
Abhay Vasant Ashtekar: Am I right about that, I mean, do you agree with this or not that's my.
wolfgang wieland: i'm a bit confused by this person second.
Abhay Vasant Ashtekar: Okay.
Abhay Vasant Ashtekar: The first view point is the one in which you do not.
Abhay Vasant Ashtekar: freeze the degrees of freedom.
Abhay Vasant Ashtekar: And therefore, you get the body form for the FLEX formulate the usual way.
wolfgang wieland: Well Okay, I would add that to that perhaps the only thing I can add is to understand how how to go from requires a local pace pace for radiative mode to the one that is defined as acknowledge infinity.
Abhay Vasant Ashtekar: So in this perspective if you go back to your slide number.
Abhay Vasant Ashtekar: Well slide number 25.
wolfgang wieland: Yes.
Abhay Vasant Ashtekar: So, so this is kind of encapsulating what you're saying right, this is the local thing that you're looking at and you're going to influence yeah but.
Abhay Vasant Ashtekar: This just for clarification i'm not on because I just want to make sure I didn't miss anything but isn't this The thing that we sort of were talking about.
Abhay Vasant Ashtekar: With the ceremony, and like 3040 years ago Okay, so this is the same as that and going to the going from the finite boundaries in an eternity that part is the same.
Abhay Vasant Ashtekar: Yes, is that OK, and the last thing was on page 21.
Abhay Vasant Ashtekar: So he is this correct gamma plus I upon gamma or is it.
Abhay Vasant Ashtekar: Because if I put.
wolfgang wieland: yeah it is.
Abhay Vasant Ashtekar: So gamma equal to is supposed to give you the.
wolfgang wieland: Oh coming to my well.
Abhay Vasant Ashtekar: Like must be i'd because otherwise it'll just go away.
wolfgang wieland: Well, it is a convention better the whole tour.
Abhay Vasant Ashtekar: or whatever you want, but I mean again I go to mind the side, and then the actual zero and you don't want that easily.
wolfgang wieland: yeah so coming into a so you're saying that today is a plus or minus.
Abhay Vasant Ashtekar: No yeah and also actually should be the other way around, I mean.
Abhay Vasant Ashtekar: To be one upon gamma gamma.
Abhay Vasant Ashtekar: gamma gamma plus I mean this is.
What.
wolfgang wieland: You see.
Abhay Vasant Ashtekar: yeah.
So.
wolfgang wieland: Okay, so in a way to to to see what's going on here is princeton's take the limit comma to infinity, then the second term goes away he's terms of ice.
wolfgang wieland: This it becomes intense or notation just a hot store, so this becomes staff even he contracted with that, so this the cutting edge and the other one is just the one where you the horse term where you replace the old student with just identity.
Okay.
Abhay Vasant Ashtekar: Okay, but my belief is that it will gamma divided by one plus gamma pi not because of what we not want is one of 116 pages in the denominator and not for page but let's forget about that, on this is totally irrelevant.
Jorge Pullin: tomorrow.
Abhay Vasant Ashtekar: Seven days yeah.
Simone SPEZIALE: I think you.
Simone SPEZIALE: Just do a quick questions and what about the beach 28 when you will give you a prescription for the indigo beauty of them etonian I was wondering if.
Simone SPEZIALE: They can be the Omega term usually can be split into something that is the delta out something plus.
Simone SPEZIALE: The XI of tea the right so i'm wondering whether your prescription effectively amounts to eliminating is it that term that is already in capital Omega or there is some part of that there remains.
wolfgang wieland: yeah I haven't thought about it in that way, because in here, so this.
wolfgang wieland: So Omega Sigma is obtained from this inflected current on Sigma while this guy is this electric current on the non hyper surface.
Simone SPEZIALE: Which and they might have a discontinuity when you pull them back, both at the corner, but.
yeah okay.
Simone SPEZIALE: And the second question, I had to maybe sort of talks also with this discussion that has been going on.
Simone SPEZIALE: i'm not writing right, could you when we think of what is in our perspective, one, so the fuller face base associated with scribe the geometric variables that the parameters this face piece or the shears.
Simone SPEZIALE: But when you think you just in terms of what you've been referring to as edge mode, so they they just the to the data can you give us a geometric characterization of what they are probably did, but can you just repeat it.
wolfgang wieland: While they're there Mozart did.
These guys.
Simone SPEZIALE: But I can you give us a Java, the characterization of what these variables describe.
wolfgang wieland: So they are described them as they come former factor, and I said to our SL to see frame.
Simone SPEZIALE: Okay, so the to the metric is basically they they degrees of freedom mother describe your reduce the face pace in these second viewpoint uh huh Okay, thank you.
Abhay Vasant Ashtekar: One minute and I thought that that extra information or site to not maybe that's what.
Abhay Vasant Ashtekar: It is.
Abhay Vasant Ashtekar: it's not related at all.
wolfgang wieland: today's no that's right sorry, there is no part in here that would correspond to say.
wolfgang wieland: These old spin coefficients not courageous.
Simone SPEZIALE: And he gives up here of these pink efficient.
Where they could produce okay.
Simone SPEZIALE: Thank you any.
Jorge Pullin: Other questions.
wolfgang wieland: You.
wolfgang wieland: Know similar maybe.
Simone SPEZIALE: Perhaps actually because.
If you think of.
i'm.
wolfgang wieland: Sorry.
Abhay Vasant Ashtekar: The fall of can say what What do you mean by perhaps.
wolfgang wieland: You Okay, excuse me so someone was asking if.
wolfgang wieland: If side two shows up in some collective potential.
Simone SPEZIALE: By yours, but then.
wolfgang wieland: When.
wolfgang wieland: The way it.
Is.
wolfgang wieland: I think it shows up in tita but then goes away, if I remember correctly, it goes away by.
Abhay Vasant Ashtekar: They don't show it.
Abhay Vasant Ashtekar: really does show in the top, one of the two.
wolfgang wieland: Exactly chose hopping Peta, but it appears in there is totally rewritten for something so that it falls out of the when we compute Omega at the simplistic to form.
wolfgang wieland: So side to a piece, because it appears in the fall of for the.
wolfgang wieland: Non affinity or Cup.
Simone SPEZIALE: As a total derivative in space or a total derivative infield spaces, so you just make sure you feel space yeah so maybe it could be preserved, if one and large the face space in some appropriate way, yes.
Simone SPEZIALE: which could be interesting yeah.
Abhay Vasant Ashtekar: But in this case, are you keeping side to fix them on the face space, I mean like right.
Abhay Vasant Ashtekar: which we point in any other two viewpoints are we keeping this fixed on the face face or you do not have to worry about it.
wolfgang wieland: um well, I did not worry about it, because it appears as a total derivative in in in face face.
wolfgang wieland: On field space on me, so there is a delta side to it just goes goes away, of course, then the question is, what is its role on.
wolfgang wieland: That that survives this question, what is it.
Abhay Vasant Ashtekar: yeah so again, is the usual thing that I have been told, is just we don't deploy constant yeah yeah.
Simone SPEZIALE: you're not fixing the area to form right, so how can it appear as just confused now how can it appear as a total variation infield space, are you interested when you define it as integral of these scupper what is happening there, that makes it.
wolfgang wieland: happen so.
Simone SPEZIALE: You may request, so I think, because your ear to form is not so.
wolfgang wieland: Thank you so Kappa shows up here, actually, you can see it in here so Kappa this goes like side to over on Oscar but epsilon goes like R squared so the two constantly charter, provided it variations of the area to form for off faster than.
Oscar.
Simone SPEZIALE: I guess that's, the key point so in your court so to go back to your question, the corner variables that you're describing that span of his face piece and you're allowed to very.
Simone SPEZIALE: Are there, let me sharpen my question are there, the leading order of the variation of data to form or the sub leading.
Simone SPEZIALE: Like are you fixing a bond, in other words, are you keeping up on the frame fixed, are you allowing varying bondi frames, to be part of your face space.
Abhay Vasant Ashtekar: I think it's getting it fixed to Bali.
Simone SPEZIALE: Bali famous Okay, then it will make sense okay yeah doesn't even make sense upside to the.
Simone SPEZIALE: South and the correct the largest one could bring it back.
Abhay Vasant Ashtekar: Right.
Jorge Pullin: Okay, mark you had a question.
Marc Geiller: it's I think it's Okay, I can ask it privately maybe.
Jorge Pullin: There is a question in the chat as well.
Jorge Pullin: So hallway dang says, I want to ask a question, are you considering, are you considering the synthetic space time here, I know, synthetic flat space time the super translation charges are the bondi mass can you model recover this result, or you recovered it already.
wolfgang wieland: yeah so the point is that.
wolfgang wieland: In here, so the hamiltonian.
wolfgang wieland: I get when calculating this.
wolfgang wieland: By integrating this equation.
Is is given by this line.
wolfgang wieland: So it is the body mass corrected by something that looks like.
When interviewed times.
wolfgang wieland: amperage so it's like a.
wolfgang wieland: relation between the body mass and hamiltonian is.
wolfgang wieland: governed by.
wolfgang wieland: genre transform into a space.
wolfgang wieland: So it's like different.
wolfgang wieland: attentions on.
wolfgang wieland: Different that thermodynamic potential in some cases.
Abhay Vasant Ashtekar: So I think the answer is that, although the transpose it doesn't show explicitly.
Abhay Vasant Ashtekar: Because transparency only talks about bond the energy and not about bond is super momentum and the question was about bond discipline momentum in some ways.
Abhay Vasant Ashtekar: But the answer is that bondage for momentum can also be obtained this framework if you're an adult the first viewpoint, for the second viewpoint, the hamiltonian is defined only up to constant and then one does not know.
Abhay Vasant Ashtekar: Unless one brings in the first few point for consistency than one would not know what the value of the body, energy or bondi super momentum is but from the first viewpoint, the bondi.
Abhay Vasant Ashtekar: sober momentum is actually recovered in this work.
wolfgang wieland: yeah I think that's fair.
Jorge Pullin: Any other questions.
Okay.
Thank you.