Jorge Pullin: Our speaker today is your system all will speak about SMS analysis of spin folders with time, like faces and new parameter ization.
Jose Diogo Simao: Yes, yeah.
Jose Diogo Simao: So of course Thank you everyone in the audience for being here, good morning good afternoon or good evening, where appropriate and yeah Let me also thank the organizers and in particular the Committee for allowing me to be here today and discuss this this work.
Jose Diogo Simao: As you can see, and also as what you just said, this is essentially a document reports on some work that I did with my PhD supervisor Sebastian.
Jose Diogo Simao: and on we recently pushed to the archive a blueprint for this, the the paper has essentially the same name as a thoughtless sm data analysis.
Jose Diogo Simao: Of spinning funds with them like faces in a new parameter ization so as you can see, this is a spin from talk and I can imagine that not everyone.
Jose Diogo Simao: And this substantially familiar with spin from so, of course, I would like to introduce these objects and discuss what they are, but before I get to that point.
Jose Diogo Simao: I would really like to start with just a one first slide where for the people that may be a bit more familiar with this things I just enumerate the number of results that we found in the paper.
Jose Diogo Simao: So, as I said.
Jose Diogo Simao: This is a spin from paper we essentially study the rather famous your model, in particular, with a so called Conrad the newbie to extension.
Jose Diogo Simao: Where the steam for model is extended to the bus of your the of having also time like faces.
Jose Diogo Simao: And the one of the essential results of the the paper are and then God fearing for comics policy drove me gossipy space time so here i'm thinking are to one another and do for me diarization for a part of the model which, as I will see simplifies the analysis in some sense.
Jose Diogo Simao: And we find that.
Jose Diogo Simao: For the amplitude of a certain part of the model.
Jose Diogo Simao: This amplitude is a semi classical level in some sense not dominated by the configurations that our semi classical expectations within some census you so this geometrical configurations.
Jose Diogo Simao: An earlier version of the of the blueprints in case that you, you might have looked at it has the claim that the cosine problem could be absent.
Jose Diogo Simao: In for particular types of extreme forms this hasn't been minimal been redacted thanks to some clarification bye bye Hong Kong Leo, to whom we are very grateful.
Jose Diogo Simao: Now I will also like to say what the goal for the Doc is just so that we're all on the same page now here we start really the the box itself, I want to in some sense argue that this particular model which is important and.
Jose Diogo Simao: In some senses, as I would like you, for this particular model with a not in assessing toxic behavior so it seems semi classical behavior with the not recover.
Jose Diogo Simao: geometrical configurations, which is what you would expect, again to have something like okay just you and this might suggest that the model needs for the constraint.
Jose Diogo Simao: But, so this is the more technical now I get to a general introduction, so this is my outline for the talk, I will essentially.
Jose Diogo Simao: would like to start with a general introduction to the to the API calls before model and this Conrad in a bit extension.
Jose Diogo Simao: So this is really rather in productive, but then I will have to dive into a little bit of technicalities any particular discuss representations of the SL to see group.
Jose Diogo Simao: Of course this is important because it's the double cover of the symmetry group that we expect in Glasgow space time and then we can discuss the syntactic analysis so, then we really look at the essence of the behavior of this model.
Jose Diogo Simao: will start imposing the problem and then understand how this new parameter ization for a particular type of the model can lead us to to this conclusion.
Jose Diogo Simao: Regarding this possible non geometry city in some sense okay good, so I would like to start, then, with this general introduction to the model, what is the general idea, what are we trying to do.
Jose Diogo Simao: So of course what we would like, in some senses to have well in some sense in every sense is to have a theory for quantum rabbits.
Jose Diogo Simao: And we can do this in the kind of naive way where we take to fit and we try to construct the preservatives theory, but of course we know that this has problems.
Jose Diogo Simao: A lot of them in particular problems with normalization and one of my think that the cost for this is because we are not taking.
Jose Diogo Simao: The lessons of general relativity to serious so general relativity has a particular property.
Jose Diogo Simao: of being a theory without any iPod structures, maybe, besides the money for them, which is constructed, which in the end.
Jose Diogo Simao: has to do with the fact that the action is very internal if you're morphosis.
Jose Diogo Simao: So we might say Okay, rather than having the opportunity description, where I have to fix a background, when I have to have an iPod structure, let me try to have something like a better tool for gravity, where I wanted to actually evaluate the bad things.
Jose Diogo Simao: Now, how do we do this, why is this your proposal initially discussed by angle and collaborators around 2007 So the idea is that.
Jose Diogo Simao: rather than looking directly at the actual gilbert's action I will consider something like the debt reduction, so this is probably familiar to a lot of you.
Jose Diogo Simao: it's necessary to see gauge theory formulated on an SF DC principal bundle.
Jose Diogo Simao: With we have some curvature to form with values on the lead algebra and then we have some veterans, and this is in some sense of first started formulation of the metric.
Jose Diogo Simao: The star here is the hardest time relative to them interesting metric the gamma is the music parameter that again i'm sure you're familiar.
Jose Diogo Simao: Now, a very useful different theory that that we might can see, there is a so called BF theory, so this is still at the nfl to see gauge theory F is still the same field.
Jose Diogo Simao: bs now just general to form with Val is also on the lead algebra and this section is particularly useful because under the imposition of some constraints.
Jose Diogo Simao: usually called simplicity constraints those ones here, you can go back to the data protection, and this is, in general, the observation that we will use to construct the spin for model.
Jose Diogo Simao: And you can see here in the boxes what the general ideas and the ideas that we did BF theory with this critize VF theory such that we have a well defined path integral.
Jose Diogo Simao: We compute the bathroom you know, this would be the quantization step and finally we apply the constraints of the quantum level that would.
Jose Diogo Simao: Hopefully, take us from BF to something like gravity, how is that done very generally again it starts with our manifold using the metaphor, has no boundary in general, and we might consider something like a seller decomposition now, in most cases, one considers a triangulation.
Jose Diogo Simao: That would be if we are considering one a few big gravity that will be in four dimensions learning so many folks I would triangulate it by for simply says here and just for fun I just put here a plane.
Jose Diogo Simao: But, in general, I can also not going to necessarily a triangulation I can also can see their public intervals complexes.
Jose Diogo Simao: Now what one does, then, is rather than constructing the theory on the server the composition when actually construct the so called dual too complex, and this is a procedure for taking my initial manifold.
Jose Diogo Simao: and ending up with some structure that has some first some faces vertices and edges, have you this picture is the general construction in the case of the dimensions.
Jose Diogo Simao: For triangulation so you feel I mentioned in the triangulation my fundamental object let's call it would be a tetrahedron.
Jose Diogo Simao: What I do is, I can see the vertex tool to the tetrahedral I can see there's some edges do will do the faces and then I can see there's some faces.
Jose Diogo Simao: Which are bonded by these edges and Abdul to the faces of the tetrahedron itself.
Jose Diogo Simao: The beach during the race is precisely that same construction, but now a bit more explicit and then I just take it out, and you have this picture here, which is probably the picture that you have seen very often.
Jose Diogo Simao: When one discusses spin false this guy here again built of vertices edges and faces will be this multi dimensional complex on which we're going to these guys are few.
Jose Diogo Simao: So we've got to repent ization step and the transition step we start to be, if I have to consider my best thing to grow, where I integrate over be but also over the connection, so this is the connection on the musical bundle.
Jose Diogo Simao: And what I do is formally I integrate out to the field and integrating out to the field this looks like what you're used to seeing for the Doc function direct delta function and we get here, then the angel of the connection and then the delta on the curvature.
Jose Diogo Simao: The dissertation step that happens on the door complex, so we have a well known theorem from differential geometry that thousand steps.
Jose Diogo Simao: If I know the death, the burial transports of the connection on the manifold I can recover the connection okay so rather than integrating over the connection, what I can do is I can essentially integrate over every possible group element associated to the edges in my dual complex.
Jose Diogo Simao: So that's the integration of very the group elements for the edges and then the curvature form becomes product off parallel transports around the face.
Jose Diogo Simao: So I just get some delta have some group elements and I have a brother for every face all good.
Jose Diogo Simao: Now this is like embraceable a well defined object now because with this criticizes, but we can further manipulated and that's where we get to this maybe famous.
Jose Diogo Simao: picture of the amplitude for spring phone and it was something like what I will show you a bit, I just want to say.
Jose Diogo Simao: That what you do here is essentially that we know that for compact lead groups there's a theorem that tells me that if I have a function on such a group.
Jose Diogo Simao: I can expand it in terms of unitary any reducible representation of the group.
Jose Diogo Simao: So to see it's not compact, but there is an analogous construction and I can see there the delta function as a kind of generalized function, I do that procedure I just send massaging I get this object here so what's going gun.
Jose Diogo Simao: On the left, what we have is and again i'm considering just for simplicity of triangulation by simply system four dimensions, but I have on the left is a general communitarian diagram of what something like a forcing FLEX might look like.
Jose Diogo Simao: So at the boundary of the force in place, we have to 200 those are these guys here who responding to a very big on the diagram the lines tell me that the triangles other tetrahedron are joined together and this gives me becoming authorial structure.
Jose Diogo Simao: Good, what does the amplitude look like after the massage, and so we have some some of our assignments of unitary irreducible representations of SL to see to the faces of the door complex.
Jose Diogo Simao: For every face, we have a brother other dimensional representation and then, if every vertex we have this object here.
Jose Diogo Simao: Now, you should think about this object essentially as a fail as a fail that you tile over the wall complex that's what I mean by this brother delivered.
Jose Diogo Simao: So I mean if you look at the vertex you place the style you look at the other vertex connected to it, the place another time and in doing so, you will join these edges here, and you will end up with loops.
Jose Diogo Simao: What does that mean well what i'm supposed to represent here is every line represents a representation of the group which representation well, the one that comes from the society.
Jose Diogo Simao: The in the blank by humans and integration oversell to see so when I put when I tell.
Jose Diogo Simao: My little complex with this object here I end up having these whoops some integrations and so when I have these traces of representations and integrations in some difficult coming authorial way.
Jose Diogo Simao: But it's a communitarian way, that is, the narrative from the community that characterizes my initial seller, the composition, so you can see that the kinetics of this guy is in some sense analogous to the Community director of the floor simplex you.
Jose Diogo Simao: Good, so this is already at this level, in principle, a model for quantum BF theory and now we go to the application of the constraints.
Jose Diogo Simao: I do not want to discuss the technical details of how you get the constraints, but I do want to say that it turns out.
Jose Diogo Simao: that the application of the constraints require a choice of a causal character at each boundary three dimensional object and what I mean by address a puzzle character.
Jose Diogo Simao: Is that one has to say, in the case of for simply says, for example, one has to say whether my country he drew within the boundary is space like or timeline or eventually find like with some space like edges some space like faces.
Jose Diogo Simao: And then, it turns out that for a certain assumption of causal character this specifies a representation of a particular SF DC subgroup.
Jose Diogo Simao: And we have many cases, the first case that was first exploring the original EPL paper which would call it kronos.
Jose Diogo Simao: And is the case where I have the two to space, like a heater together and again we're looking at interfaces so what I mean by interfaces when I go to that are here together along the line.
Jose Diogo Simao: This was originally girl case and it was later generalized by Conrad the mvp the to this coronal case to the Federal Criminal case into this Eric Renault case.
Jose Diogo Simao: This case here is the one that I will particularly mentioned today is the case where I have time like bala he'd read john together as time like faces.
Jose Diogo Simao: Good so what it does, the model look like in the end, what did what happens is that the these constraints and up.
Jose Diogo Simao: singling out particular sets of admissible representations and this depends on the skull characters so the representations of SL to see are labeled in some sense by two numbers European n.
Jose Diogo Simao: will discuss this later and what the constraints do is essentially they tell you okay can see that only specific ones.
Jose Diogo Simao: That are specified by some function and the ones that you can see the do depend on the causal character.
Jose Diogo Simao: That you assume OK, so the final model looks something like what you see here where now, the system is constrained to only those admissible representations and the misrepresentations depend on which interfaces here, you were considering okay.
Jose Diogo Simao: Now, one thing I would like to say is that, although we started with a very geometrical theory at this level, there is really no notion of at least the classical geometry you want can argue that there's maybe some fuzzy geometry but classical geometry just.
Jose Diogo Simao: Actual tetrahedron or an actual forcing blake's he's not there anymore, what we have is, we have some coming weeks.
Jose Diogo Simao: We have some representation theoretic data, and we have some weak notion of causality what I mean by this is the causal character of the beaches, so this is essentially what I mean by this girl corner, maybe the spring from other.
Jose Diogo Simao: Questions of what the what the actual.
Jose Diogo Simao: Operational meaning of this is and how to interpret stuff like tradition amplitude that's that's another problem that I will perhaps not discuss today, but those are interesting question.
Abhay Vasant Ashtekar: Can I just ask a question about this issue, precisely.
Abhay Vasant Ashtekar: The.
Abhay Vasant Ashtekar: This time, like what's the space like etc.
Abhay Vasant Ashtekar: Is that referring just to the kind of the Interior, as well as the the boundaries, so to say if you're calculating the transition amplitude.
Abhay Vasant Ashtekar: Then there'll be some boundary so is is this referring to the Tetra hydro on the boundary or also in the interior and you're not considering a single single for simplex here is that correct.
Jose Diogo Simao: For now i'm like well, actually, so I will discuss in general now in the following, I will restrict to one single for simplex, but at this stage, this is, in principle, valid for the whole many for which can be translated by many for simplicity.
Abhay Vasant Ashtekar: Right, so if you have many for simplicity's then Is this something is this restriction on every face inside the one.
Abhay Vasant Ashtekar: audio on the on the boundary.
Jose Diogo Simao: It would be so the application of the constraints require knowing the causal character and what that means is at least as far as I understand the the corner the maybe the.
Jose Diogo Simao: model, what I would say that means is that you might expect something like sending over possible assignments off causal character in the book and having done that Council character already specified by the boundary data at the boundary of the main.
Abhay Vasant Ashtekar: OK, so now you're assuming that all the the faces that time like bought in bulk as well as in the boundary.
Jose Diogo Simao: not yet, but in the following for the discussion.
Abhay Vasant Ashtekar: yeah yeah Okay, thank you.
Abhay Vasant Ashtekar: Good.
Jose Diogo Simao: So, then we can move on having introduced the girl can only be the model and now again some technical discussion on this slt see stuff which will be useful, because of the discussion here this guy this new parameters like this different parameters.
Jose Diogo Simao: So the representations of SL to see, they are constructed on homogeneous functions in situ and what the artist i'm a genius functions, is essentially functions.
Jose Diogo Simao: That have some certain scaling property, so if I scale my argument, the image skills in a particular way labeled by this and one and two numbers.
Jose Diogo Simao: And then the representation is constructed on these functions, simply by taking by essentially changing the movement of the function to God finger on.
Jose Diogo Simao: This Z which lives in CT now, we will focus on the principal series which is particular.
Jose Diogo Simao: subset of the representations, for which the scaling number satisfy this particular property and it's common to re label, then this and one in into by this and and the road where an integer and really is a real number.
Jose Diogo Simao: And there's some relationship between between this and row, and the other one and then.
Jose Diogo Simao: This principle series is unitary that's why they're useful first it's unitary under a given inner product it's the inner product that you can construct using the canonical volume pharmacy to and you integrate over the complex projected space.
Jose Diogo Simao: Complex reactive like.
Jose Diogo Simao: Good so Now the question is.
Jose Diogo Simao: For the the application to the Conrad and maybe their model we have to understand how to relate principal serious representations to unitary any reducible representation of Su one one in Su to being those the subgroups of relevant interest for us.
Jose Diogo Simao: And that's what we discussed now so because the homogeneous function satisfied scaling property.
Jose Diogo Simao: I can know the whole function, by defining them on either the sphere s3 and that s3 is if you're free to ask you to.
Jose Diogo Simao: or on the sugar library life and H3 which is here, characterized in this particular way down taking plus and minus one values and choosing the one of the sheets of paper not again that every every each such sheets is a morphic to Su one one.
Jose Diogo Simao: This is essentially the basic fact that we need to establish this correspondence between SL to see and the sub groups at the level of representations and, indeed, it turns out that their existence as a more efficient.
Jose Diogo Simao: Between the critical series of SF DC and two copies.
Jose Diogo Simao: Of the scrape that will functions on s3 one one and then not all of them, but those that satisfy a certain covariance property, so this is just some transformation property for the function it doesn't really matter why two copies well it's because we have this to shoot electrically.
Jose Diogo Simao: And then there's a second and bless your ltv theorem that relates, the screen double functions of Su one one and the continuous series and the discrete series of unitary irreducible representations of so you went wrong.
Jose Diogo Simao: And that's enough, because what we can do, then, is, we can establish this correspondence between the principal series of SF DC and the discreet series and the continuous series.
Jose Diogo Simao: of unitary irreducible Su Su one one representations good the same thing can be done with us, you do and, indeed, what we can find is this so called canonical basis, so I have a completeness relation in this.
Jose Diogo Simao: Principle serious space involving the unit every every just a representation of Su to level by the Jason AMS that you know from YouTube.
Jose Diogo Simao: And they have a particular way of taking in Su to representation matrix and constructing and i'm a genius function from it.
Jose Diogo Simao: The same thing holds for us one one this is now called pseudo basis because of a pseudo sphere, and they have a way of taking my astral one one representation agencies in either the continuous series or the script series and recovering a homogeneous function in SL to see.
Jose Diogo Simao: What can I use this for so recall that we have in our formula for the partition function, we had are failing essentially I can use this to isolate that time so.
Jose Diogo Simao: What I can do is I can come here to my to my title at each vertex and remember that.
Jose Diogo Simao: This thing by itself doesn't mean anything, this is not a number, it means something when they're all together and forming groups and so on.
Jose Diogo Simao: But what I can do now is I can come here, I can apply my completeness relations at the end of these of these these edges here of this links and in doing so.
Jose Diogo Simao: I end up essentially with matrix elements with sandwiches so what I mean by a ball here in a bowl here is essentially here have a state from a completeness relationship, I have another states and this thing here is now a number, or at least the functionality.
Jose Diogo Simao: In this way I can go from the tiling to actually isolating an object which lives at every vertex and in such way I construct the so called vertex amplitude for speed.
Jose Diogo Simao: In a less pictorial way and in a way that did that, to my general Community oryx even those that are not necessarily coming from a given all the hero, the composition of the manifold because, of course, then I can say.
Jose Diogo Simao: I can take this things up the step and say okay now i'm going to consume every possible communities and so on.
Jose Diogo Simao: And I do have a formula them for the vertex sample to have the spin from involving some SL to see integrations.
Jose Diogo Simao: Some delta function that is here to regularize the integral essentially which doesn't really matter for the conceptual understanding and then these inner province in the South to see principal series space which can precisely from these lines here okay.
Jose Diogo Simao: Good, so now we have the verdict sampling what we want to do is understand the semantics of this right example, so we want to understand what something like it's semi classical behavior because look like.
Abhay Vasant Ashtekar: Can you say something about convergence of getting to the last transparency, the one before yeah.
Abhay Vasant Ashtekar: yeah.
Jose Diogo Simao: There, yes, sorry, could you repeat that sorry.
yeah.
Abhay Vasant Ashtekar: I mean, does it integrate on a non compact space you've got all these numbers which are.
Abhay Vasant Ashtekar: There any bounded ness on them is not there, because the group is not compact So what about convergence of that interview.
Abhay Vasant Ashtekar: Because I didn't do exist.
Jose Diogo Simao: My honest reply to this is, I do not know whether this this interval actually converges and I would honestly thought that it does.
simone: um wait, yes, I mean you just have to write the.
simone: N minus one instead of n is one redundant integration that you have to eliminate but, once you have done, that there is a notion of integral graphs on which today.
simone: The example to this finite and for the case of the first simplex is that'd be improved by balletic rainbow the their model, and then I think john and Roberto maybe proved it for the beer and model.
simone: So the important thing for the is just that you remove one I don't I didn't Iran and then for diverting something that is fine for the for simplex.
Jose Diogo Simao: For the vertex yeah I guess that, then you can see there's more than one for simplex there's already been some over the representation.
simone: Sure, but I thought you were talking about just the integral yeah yeah we are, we are, yes, yes, yes.
Jose Diogo Simao: Yes, thank you yeah.
Abhay Vasant Ashtekar: So, but but is that the characters, which is a correct answer removing one or leaving it as it is.
Jonathan Engle: It is correct, the way it is because he has the delta function in there, the delta function has.
Abhay Vasant Ashtekar: isn't removing one okay.
Abhay Vasant Ashtekar: Thank you.
yeah.
Jose Diogo Simao: anyways with respect to either this vertex sample for the single for simplex or with the holding 12 for the whole model, even if the danger of is not converge.
Jose Diogo Simao: At least it might be this.
Pietro Dona: Can I can I ask a question.
Pietro Dona: On on the same topic.
Pietro Dona: So, probably is a yes, no question, maybe for john that just commented, I am familiar with.
Pietro Dona: The work that proves that that completed this convergence is finally.
Pietro Dona: Was the proof the pendant on the particular boundary so is the proof valuable so for non.
Pietro Dona: Space like ponder.
Jonathan Engle: it's a good question and I don't remember I would need to go and review the proof again but yeah we only approved it for space like boundary for the simplex that's true.
Pietro Dona: Thank you.
Hongguang Liu: Actually, actually recently, we have a proof for the for every woman space like under its base steel space like physics, but for the ice on one tetrahedron we see our planet and the convergence in for the single word X.
Pietro Dona: Well, thank you very much.
Hongguang Liu: yeah the people he's he's almost ready.
Jose Diogo Simao: Okay, good, thank you very much for for the insights.
Jose Diogo Simao: So where was I.
Jose Diogo Simao: yeah yes okay so so we, we do have the the vertex amplitude now, and now we want to understand what something like semi classical behavior might look like.
Jose Diogo Simao: What does that mean we essentially wanted take that funnel that we had there and we want to understand what happens when the spins arbitrarily large so we want to take a uniform scaling.
Jose Diogo Simao: Of the spins again you don't so considering every possible spins coming from Su Tu Su and one discreet, and this one continuous.
Jose Diogo Simao: And what I want to do, then under this uniform scaling is, I want to take my vertex amplitude and I want to write it in some form which is adapted to something like nothing got the expansion of the integral some something like a stationary face approximation.
Jose Diogo Simao: So what I want to do, then, is once I have this one here, I want to fix the boundary data, so this means fixing the spins and the state's those black dots that day that I had in the picture before.
Jose Diogo Simao: And then can see there my stationary critical point conditions, what what those involved, so we have integrations over so to see so I have to concede there a variation on the group.
Jose Diogo Simao: And they also have this new brother in the visible series space, so I also and if you'll remember this was an integration.
Jose Diogo Simao: of a complex projected line, so I will also have some some screeners.
Jose Diogo Simao: And then, I have a maximum ality condition on the real part of the action but, since it has been proven before that the the action for these cases is always know non positive it's sufficient to require that the real bite vanishes.
Jose Diogo Simao: This construction, so this idea of the synthetic study has been done some to be a sufficient number of things before actually so it was initially done by Barrett.
Jose Diogo Simao: In the cleaning up our model, but also for the lower end soon gates around 2009.
Jose Diogo Simao: Without the Conrad the maybe the extension and then extended by Kaminski and collaborators more recently.
Jose Diogo Simao: For the other cases, leaving the this case here that we're going to discuss a very open Okay, and then my recently by a new enhance precisely for this this case of time like faces, this is so, these three words are essentially the main stepping stones, on which we we worked fine.
Jose Diogo Simao: Okay, so if I went to understand this guy I need to have an expression for so forth, and so on.
Jose Diogo Simao: And if I want to do that, in particular for the background interfaces that that will be considering I need to explicitly be able to compute The thing that you're serious going to build for this evening.
Jose Diogo Simao: So I need to be able to compute this particular expression of the boundary state and some action of so when one of us up to see there and also here with a complex country finding this existed expression is what i'm going to focus on now.
Jose Diogo Simao: So that's where this event registration comes along so again, the states that we are considering at the boundary there SLC states induced from a continuous series state of the art of so one one.
Jose Diogo Simao: Now, in the original formulation of the gun rather new be an extension what one uses for these states are states that are in the agent basis.
Jose Diogo Simao: Of this game one generator, so this is one of the generators of so one one, so I have them here that you can think of two three as the rotation generator q1 and q2 as boosts day one is not compact.
Jose Diogo Simao: And because of this, the states of q1 are not in the representation space, and so one actually needs this generalized second basis construction discovering drupal construction.
Jose Diogo Simao: which was initially done by link blood in me Joel and and 1970 So what do we have we have decentralized states jail under Sigma which are labeled by the chasm you J where J is continuous complex it's a complex number, with a continuous pyramid there s and a real constant part.
Jose Diogo Simao: And then the value of K one is a Lambda which leaves the real line, and we have something like a buried the operator, where the Sigma labels and minus one in a plus one, I can tell okay.
Jose Diogo Simao: Now, of course, if I want to do now, if I wanted to pick the model and understand it's it's excessive tactics and plugged into that from that I had before.
Jose Diogo Simao: It is conceivable that different choices of basis will lead me to different explicit expressions which might be more or less useful, the end result has to be the same, but I might have more.
Jose Diogo Simao: or less useful particular expressions expressions, and one of the apparently.
Jose Diogo Simao: What the literature, has shown very clearly that he said for a semantic analysis, the most useful basis, you can see, there is a basis of the so called good human states.
Jose Diogo Simao: What I mean by this is, I take my state I think some reference state, so I take some particular.
Jose Diogo Simao: alumna here that's what I mean by the head I think some particular segment here, and then I let my Su one one X on this state and essentially generate the whole the whole space.
Jose Diogo Simao: And indeed, this constitutes and over complete basis and there exists a completeness relation, for the continuous series of so one one.
Jose Diogo Simao: Now again by the same arguments that that I just mentioned, there might be more useful or less useful.
Jose Diogo Simao: choices, and we have to choose which particular choice of reference state land and see where we pick.
Jose Diogo Simao: what's Conrad the and maybe the do in the original papers to say Okay, we are interested in what is what might be in some sense the most semi classical.
Jose Diogo Simao: Looking states and do this by looking at the variants of the kazimir and all the fighting.
Jose Diogo Simao: What they find by doing that these this relationship where they say Okay, then my reference London is going to have this grabbers relationship with us where again s is this spin.
Jose Diogo Simao: And they'd be Sigma they come they choose the Convention my Sigma is equal to one in originally brl case.
Jose Diogo Simao: And if we think about Su spins what we have is that the reference magnetic number m was chosen to be changed, so this is the this way the maximal weights representations and this looks.
Jose Diogo Simao: Completely aesthetically perhaps a little bit more complicated than that we wanted to maybe go around this and that's where the synchronization comes in.
Jose Diogo Simao: And it was already noted by by link blood in his original paper that the differential equations that characterize the eigenvalues of this generalized I can basis at the meet the complex solutions.
Jose Diogo Simao: So, although it does, then, is when he goes to the complete this intersection ality relations to prove this nuclear spectral theorem he fixes Lambda to be real.
Jose Diogo Simao: What we show is that we can actually still have a completeness and Arthur banality relations by taking Lambda to have a constant imaginary bite.
Jose Diogo Simao: And in the completeness relation involving the jail on the Sigma states, but also the J conjugate London Sydney mistake, and if you can show that there is a completeness relation.
Jose Diogo Simao: With the States.
Jose Diogo Simao: And there is an orthogonal ality relation with the state's you might be thinking, but the one has to be self a giant.
Jose Diogo Simao: plugins have complex Sagan valleys and again this is one of the nuances of the skull fungible construction, these are not states in the original representation space they are.
Jose Diogo Simao: Akin states have an extension of your way to this larger space on which again construct the States and in the extension of your one is not self the job, but everyone.
Jose Diogo Simao: In the original representation space is and indeed that contribution of London is essential to maintain the self judgment self care one in that original representation space.
Jose Diogo Simao: can be seen by considering the inner product in that original continuous series representation space so you'd like some science and fight day one, you like the text on the phone.
Jose Diogo Simao: You can write this as this integral where the F is a distribution associated with this new Generalized vegan basis.
Jose Diogo Simao: And you have to have the bunch of Islam that they're such that this conjugation cancels with this stuff modulation here the Lambda factors out, and this is the same result as acting with K one directly on this state here Okay, so when did you have suffered joining us of q1.
Jose Diogo Simao: Now what you can do, then, is you go back to the requirements of currently and maybe the of having have normally find this experience of the chasm you.
Jose Diogo Simao: And then you have actually a whole set of solutions and among a set of solutions with big by hand because this is the one that will simplify our equation substantially with big by hand Lambda equals AJ.
Jose Diogo Simao: And Sigma wistful livid to be one and again compare with the perhaps simpler girl choice of the maximum weight states.
Abhay Vasant Ashtekar: Do you see what the motivation is for going to complex, I mean what was wrong with the original.
Abhay Vasant Ashtekar: Yes, yeah.
Jose Diogo Simao: Yes, so the problem is that.
Jose Diogo Simao: This is hard to argue without showing that the actual finalists, so this is essentially a technical problem, there is no I would, I would say, there is no physical.
Jose Diogo Simao: heuristics or motivation to go to the complex I can states, I can I can balance, why do we do so.
Jose Diogo Simao: We do so because, essentially, as I said, we need an expression for the United States, the expression, the way of recovering the cell to see from the Su one one representations is rather involved and it contains some hyper geometric functions.
Jose Diogo Simao: For the EPL case and for the other cases study.
Jose Diogo Simao: You know, bar bar this original interface, the maximum weight case is always such that those hyper geometric functions simplify into polynomials they simply disappear.
Jose Diogo Simao: This choice by Conrad the maybe that wasn't so so you simply have the hyper geometric functions there, and if you wanted them to study the aesthetics.
Jose Diogo Simao: You would essentially have to make an approximation and synthetic expansion for lunch spins already by at the stage of the finding the boundary states.
Jose Diogo Simao: So this is precisely what they want to show, and what it can do so this is a technicality, so the expression for say under this different dramatization.
Jose Diogo Simao: Actually, simplifies into polynomials and we have an explicit expression that does not require an essence expansion, that is valid for large screens so that's precisely the.
Jose Diogo Simao: Incredible work that blue and handed in their paper, they simply they took the prescription of underwriting either, and they sort of follow through and yes and optic analysis they.
Jose Diogo Simao: They expanded they do the messenger expansion for lunch spins of the binary states.
Jose Diogo Simao: Now I have here a screenshot of the paper it doesn't really matter what the particular object so here, I just want to maybe show you an aesthetic where I do aesthetically.
Jose Diogo Simao: Show you somebody aesthetic perception of the States here on the top, these are the States constructed.
Jose Diogo Simao: For the URL case they would rather simple, this is the case for the for the actual coronal and your soprano case, and this is now the States this is the expression for the States and the Disney privatization.
Jose Diogo Simao: Where Now we have this expression, and we have some other expression that is constructed, with the dual number, and this is not simply the complex conjugation of the first one.
Jose Diogo Simao: so good.
Jose Diogo Simao: Now we can put everything together and kind of strike, like everything together and remind ourselves what we were doing so we're focusing on this particular interfaces that.
Jose Diogo Simao: appearing the vertex amplitude and what you want to do is you want to take this word temperatures and write it in this particular forum where I have my integrations of ourselves to see my integrations will receive the.
Jose Diogo Simao: Excuse me.
Jose Diogo Simao: And something like it refactor function something like connection.
Jose Diogo Simao: The paragon election so far those states that we just discussed reduces to this simple expression here without any approximations and just so that we're all in the same.
Jose Diogo Simao: place, let me tell you what every object in here is so the gamma is again the music bear me through the S is a spin this thing that rescaling.
Jose Diogo Simao: And then we have some Z spinner institute appearing there, remember that this comes from this interesting so to see here, we have some group integrations come from there.
Jose Diogo Simao: And then we have some H a bs and what these are, these are the astronaut one group elements fixed by the boundary data which were using this construction of the human states if you might remember that l minus appearing here is innovation that already goes back to to enhance.
Jose Diogo Simao: What this means is that I left my hdd that is again boundary data choice, acting on some reference states in situ.
Jose Diogo Simao: The bracket notation here with the Sigma three means that I take this contraction with symmetry in the middle.
Jose Diogo Simao: This thing is our action and i'll be objective is to take the Greek point equations look at what we find and essentially get some geometrical intuition.
Jose Diogo Simao: So, first of all, not that the action is purely imaginary and this already agrees with the expansion that Lou and handed.
Jose Diogo Simao: They also find funding their expansion in imaginary action and what we start by doing is we start by addressing this is thinking that the beard there this this object is GHz in terms of some parameters Alpha and beta.
Jose Diogo Simao: We start by doing this, this often, but it will be important in the fall.
Jose Diogo Simao: And we find your find some variations this ah l is essentially a generator a vessel to see which I can Burma tries using the generators of seo one one, and then I times the generators for this one.
Jose Diogo Simao: And this will be fine for me the critical points with my by vector constraints i'm calling them by vector constraints.
Jose Diogo Simao: Because they will give me by vectors as we've seen the moment and what i'm calling closure conditions, these come from myself to see and again we'll see in a moment, well why i'm calling them closure conditions.
Jose Diogo Simao: So let's start with the second ones with the closure conditions.
Jose Diogo Simao: What you're looking at again if we think, in the case of the the forcing bikes just so that it's a bit easier to visualize we're looking at the grouping to go so they're coming from this part here, so now we're focusing on this part of the day.
Jose Diogo Simao: The equations give me some some with some skins of this object without minuses and helpless again the old minuses encoded binary data.
Jose Diogo Simao: And then I had this email, which was that barometer, up to now and specify and then some other object here, how can we get geometry from these guys well essentially the ltv where the action is 111 l plus minus so let's look at l plus minus isolated.
Jose Diogo Simao: These guys are Eigen states of the key one generate So if I write this is your brother can see through here, I have some number, this is the eigenvalues of q1.
Jose Diogo Simao: Of this state, and then I have space like unit vector that lives on the space like I particular now we know that's the Su and one of them is is a morphic to our two one.
Jose Diogo Simao: And we know that the joint action is a nice on the tree What that means is that I can take this guy here X with the edge on the action by taking Su and one minus one as one one.
Jose Diogo Simao: You can show that this can be written like that which is precisely what appears there, and because the agent actually is a nice on the tree.
Jose Diogo Simao: By the edge and action I take my need space like vector and I generate the whole space, like a particular.
Jose Diogo Simao: I mean the under a particular parameter ization if you might speak for the group elements, you see that this object here is indeed very much rising up to this number.
Jose Diogo Simao: The unique space, like a particular so, then the closure condition this somewhere on top involves two types of vectors that involves this particular vector which I call me at.
Jose Diogo Simao: which lives in a space, like a regular and then also this part here which lives in the positive or future directed light account, so this is an old vector.
Jose Diogo Simao: Good what can we do with this now, we need to separate the real and imaginary bites and in doing so, this is what we find we find two different conditions.
Jose Diogo Simao: On the first condition you're going to have a similar response, I have some space like vectors and some know vectors times this imaginary part of the beat up.
Jose Diogo Simao: On the right, I just have a symbol for North vectors the real part of beat the here can be made to vanish under a particular choice of that they'll bury meters, you might not remember what the doctor and meters, where they are in some sense.
Jose Diogo Simao: Rather than related to the seo and run representations and it goes back to the Dow that was used to distinguish between the two sheets of the hyperbole, of the three of the three hyper V realized that is if your market to sql one.
Jose Diogo Simao: However, we cannot impose.
Jose Diogo Simao: cannot find or argue that these dynamically, the case that the imaginary part of visa would vanish.
Jose Diogo Simao: What does that mean.
Jose Diogo Simao: To see what that means let's first can see that the case when they mentioned it, but they'll beat that does that so let's think about those configurations, for which the imaginary quite a bit easier.
Jose Diogo Simao: In that case, we can use mean gaseous theorem we have extended in the paper we essentially proven gaseous also in our two one.
Jose Diogo Simao: And why it says is the following that if i'm given a number of vectors and a number of areas in our to one here areas are positive numbers.
Jose Diogo Simao: And if those vectors are not all co planner and they're not know, and something like a closure condition holds then there exists a unique convex policy drunk enough to one up too rigid motions okay up the translations in particular.
Jose Diogo Simao: What that particularly means is that, then, if for the particular case when the imaginary part of it is equal to zero.
Jose Diogo Simao: I can simply take my pleasure condition to imply that the sum of some spins and some space like vectors are zero.
Jose Diogo Simao: And that allows me to reconstruct uniquely a time like all the heat drone with time, like faces where the vectors are orthogonal to the faces their space like and the spins the note the area.
Jose Diogo Simao: Of those two dimensional bala here again on the left, I have the Community article structure of the simplex on the right, I have the cube This is just for visual simplicity so let's call the the configurations, for which we can apply, because the syrah as geometrical configuration.
Jose Diogo Simao: Did you already see now what the problem is, is that in the eventual isotopic expansion.
Jose Diogo Simao: I have to consider every possible configuration and for the configurations when they mentioned or deleted there's nothing I will have some some involving know vectors and then my geometrical interpretation via the Make of security Center last.
Jose Diogo Simao: Good let's go now to the I vector constraints, so what we're looking at remember the by vector constraints came from the variations with respect to Z those were the.
Jose Diogo Simao: The integrals of the inner brother King so to see so that's this part of the diagram we have some some formula from the variations and again we still have this parameter ization of gap of Z in terms of this often before.
Jose Diogo Simao: You can show that, for the particular geometrical configurations.
Jose Diogo Simao: This implies a particular quality involving SF DC generators and particular by vectors where these five vectors have some all regions structure of being constituted by.
Jose Diogo Simao: The wedge product of the M vectors that we're focusing on to the faces of our ball, the heater and this particular vector which is units.
Jose Diogo Simao: And you can already see how this can in some sense already be labeling my time, like all the heat right, it could be something like might not have multiple times, like all the heat on.
Jose Diogo Simao: Now, under the canonical spin homomorphic which takes myself to seeing projects if down to the connected component of the identity of the largest group.
Jose Diogo Simao: You can show that this guy here implies the by vector constraints, so this is why we call them by better constraints involving again the projection of SF DC onto the Lawrence group.
Jose Diogo Simao: And this wedge product of a certain unit vector and a vector encoding the normals to the faces of the Bali phaedra.
Jose Diogo Simao: Good say here is just some fixed so three rotation matrix it's fixed it doesn't really change anything.
Jose Diogo Simao: And now, having these web editor constraints, we can try to assign to the magenta geometrical meaning.
Jose Diogo Simao: We can do that by going back to closure so again this part of the diagram for geometrical configurations gave us closure.
Jose Diogo Simao: So it allows us to reconstruct our three dimensional policy drip given that our boundary data is in the conditions of the mean girls good feeling, particularly to ask it cannot be the general.
Jose Diogo Simao: Now, what we can do is we take up all the Hydra and we embed them in Madagascar space time now to one in a particular way, so we look at our rotation group elements here and we embed this guy in mikulski such that.
Jose Diogo Simao: The normal to this this time Inshallah he drunk is given by the action of the group on this is your one vector and such that the normals to the faces I also.
Jose Diogo Simao: given by the additional G acting on this m zero vector Okay, if you do so, then the ivector interpretations have an immediate geometrical meaning and the immediate geometrical meaning is that the by vector equations.
Jose Diogo Simao: involve by vectors which contain the normal to the polycom and the normal to the face and does the I vector itself.
Jose Diogo Simao: labels are represents the two dimensional hyper surface that characterizes the face of a given policy drone and this equation that tells you rotate the policy john a and rotate the ball he don't be such at the faces agree.
Jose Diogo Simao: So the vector constraints, then give us a prescription for gluing got three dimensional objects along some faces according to the particular community article structure of this graph.
Jose Diogo Simao: I will.
Jose Diogo Simao: Make the parenthesis that's one way to do the link.
Jose Diogo Simao: is again think about for simply says one way to the gluing is to glue our tetrahedron together, such that you recover for simplex.
Jose Diogo Simao: But then other way in front, I mentioned another way of doing it, however it's very simple to put all of your tetrahedron together inside each other.
Jose Diogo Simao: And that's the general configuration that then we have seen the dimensional subspace and that's what usually called the literature as a vector geometry So those are also possible.
Jose Diogo Simao: Which so this now allows us to.
Jose Diogo Simao: proceed to our discussion, but we can get from this so again, the point is that the amplitude for bernal interfaces which reads something like this in this form, adapted to the essence of expansion.
Jose Diogo Simao: is dominated for the particular case when they mentioned a part of me to vanishes by groupings of 3D complex Paula heater into for the ball hero complexes and it's not written but it's important dimension also the vector geometries.
Jose Diogo Simao: The going respects the prescribed coming to fix that comes from the model and the to the areas are given by the spin so our aesthetic are taking the scenes to be able to really large has an interpretation of taking our areas to be able to join.
Jose Diogo Simao: We can take them different before the action that we had before, and essentially plug in the geometrical configurations, and what we find is.
Jose Diogo Simao: Some some some over spins and then some angles, where this angles, are now did they he dropped angle, so the angle between the normal of one bullet heater and the number of the other Bali he'd run that's good.
Jose Diogo Simao: that's good to the first bullet here, this is precisely the area okay Jay action that you might know in its in some sense what you would expect.
Jose Diogo Simao: As a semi classical behavioral symptoms, you also have an additional term that includes this alphabet meters, which I would call it something like a Punch correction.
Jose Diogo Simao: The main point, the upshot is that the non medical configurations when they mentioned everybody to be to vanishes are unfortunately not leaving.
Jose Diogo Simao: Meaning that not all the configurations that come in that that with a basically dominate the bath integral recovery data geometry foreclosure boundary data.
Jose Diogo Simao: And this suggests that this, since this is something that doesn't happen for all the other types of interfaces This suggests that the model might need some some further constraint, so this is the discussion for the action here, we also can plug in the critical points for F.
Jose Diogo Simao: What do you find for F is this formula here and is some pre factor that depends on the spins.
Jose Diogo Simao: And what is interesting is that again it shares the same analytical features that the approximation, by the way, man have so we have the same branch structure, in particular, where we have this bench points here for the one half.
Jose Diogo Simao: Now, the problem is that the branch points the quiz side with the critical points with, in particular with the geometrical few critical points.
Jose Diogo Simao: and worse than that because of this part here the function is indefinite you have some zero over zero after the critical geometrical configurations.
Jose Diogo Simao: And the problem is, as far as we know, we don't know of any theorem in the literature.
Jose Diogo Simao: For the symbiotic expansion of multi dimensional integrals that include the situation where the critical point in the action or less with branch points of the brief vector function.
Jose Diogo Simao: Which means that we do not really have an explicit this into the formula for the barrel Colonel interfaces and this absolutely needs further research, so this is something that we would like to understand better at some point.
simone: It also mean that these non reggie configuration could be suppressed by the branch cartoon front door, this is something that you know already you can exclude this possibility.
Jose Diogo Simao: I would say that, in all honesty, a better understanding of the the actual behavior of this branch fights goodfellas that in fact.
Jose Diogo Simao: Those those magic configurations, not to clear this up to now, though, since there is this qualitative difference between the paranormal interfaces and all the other types of interfaces I would say that it's at least a bit worrisome.
Jose Diogo Simao: Good, so I am essentially at the end of my talk.
Jose Diogo Simao: But with regards to this, I want to make an artistic arguments to.
Jose Diogo Simao: Why the simplicity constraints might be failing and this goes back to Conrad and so after Conrad he be the.
Jose Diogo Simao: got their paper on the on the extension sometime later can read the also published a paper, where he was essentially arguing that there are many ways of imposing the simplicity constructs.
Jose Diogo Simao: The original way was by the weekend position of the constraints, so it was a new position by taking expectation values.
Jose Diogo Simao: and watching shows in this paper is essentially hypnosis around something like the master constraint, which is closer to the original material construction.
Jose Diogo Simao: So the simplicity constraints for is one one according to come ready with something like this and, again, these are the generators of this one one, these are some other and generators.
Jose Diogo Simao: And just as what happens in the original URL case you cannot directly struggling positive constraint, because the algebra doesn't close.
Jose Diogo Simao: What the way you can consider it as individual burial case you should consider a master constraints, so you take something like the square of the constraints.
Jose Diogo Simao: For the sql one case what Conrad he does is, you can see there's this contraction of the constraints, with the this kind of mikulski type matrix, you will have ones and minus one.
Jose Diogo Simao: Anything man that the States are annihilated by that constraint.
Jose Diogo Simao: And then these kind of shows this must reconstruct condition is precisely gives the process of the same results, the same constraints on the representation.
Jose Diogo Simao: That the weekend position does, but the problem is that why only the variable case where you just contract the seeds.
Jose Diogo Simao: You have a some of squares of constraints, such that, if the master constraint vanishes already classically, then the classical the constraints also manage.
Jose Diogo Simao: Because of this eat that here it's already the case classically that the vanishing of the master constraint does not necessarily imply that the constraint vanishes.
Jose Diogo Simao: And this was something that was pointed out by con ready and that paper, he said something like well the since we find the same thing as we did for the weekend position of constraints and we trusting we can position of strength we assume that this is not a problem.
Jose Diogo Simao: I would argue that, realistically it's at least possible that this together with the discussion that we just had might.
Jose Diogo Simao: hint that there might be something going on with how the simplicity constraints are applied for the last one one case any particular getting problems for the burger and all the interfaces.
Jose Diogo Simao: i'm finally at the end of my talk so just a quick summary.
Jose Diogo Simao: What I tried to argue, is that it is possible to find an alternative parameter ization of the model, giving us explicit expressions for the action and for the states the banners states.
Jose Diogo Simao: That there exists in gusty theorem for context for the heater in mikulski.
Jose Diogo Simao: Three, there are two one space time again parenthesis, we only show this for three dimensions, we were not able to show you so if I mentioned, but in any ways.
Jose Diogo Simao: For the syntactic analysis that's what we need is for dimensions and we showed that at least recently the employee to.
Jose Diogo Simao: does not seem to be dominated by this geometrical configurations because of the presence of the knowledge actors, we also don't yet have, in all honesty, good control on the explicit a synthetic formula for the background on interfaces.
Jose Diogo Simao: I would say that the output, then, is that I would expect that, if one understands better how the appearance of those know configurations of those no time like red.
Jose Diogo Simao: Light like vectors could be related to failing of simplicity, this could lead the way to perhaps further constrain your model and remove those configurations.
Jose Diogo Simao: that's all I have to say thank you very much for your attention.
Jorge Pullin: questions.
Abhay Vasant Ashtekar: I have a question, both of the speaker and Community listen Monet other people were worked on this extensively.
Abhay Vasant Ashtekar: I mean, is there some compelling what is the general viewpoint that one should consider.
Abhay Vasant Ashtekar: more space like, as well as time like faces, and that is absolutely essential, or that it's not essential when it is exploring the various possibilities.
Abhay Vasant Ashtekar: What is it a viewpoint kid I mean if I could, I take the viewpoint that say these results, become more for than it did you say that.
Abhay Vasant Ashtekar: One should not consider a time like cases and then you know, one can just focus on the space like what is that a viable idea or is that something wrong with it.
Jose Diogo Simao: I would definitely want to give the opportunity for other people to to give their their insight into this, but I maybe would like to just say one or two points, so the first one is the most generic argument that that I can think of is that.
Jose Diogo Simao: You know, in the same way that I keep that going that it's essential to take these fundamental lessons or general relativity.
Jose Diogo Simao: In a quantum theory of gravity, I would say that allowing for every possible causal character follows in that kind of.
Jose Diogo Simao: line of thinking, but this is a very, very basic argument that can be discussing many ways, of course, and then it may be more.
Jose Diogo Simao: In a more relevant way, I would say that having other types of interfaces and follow up sequences or whatever.
Jose Diogo Simao: could be important if one is interested in matching just be from formalism to other families is that exists, so, for example, the causal dynamical triangulation symbolism, where they have the space like hyper surfaces, but then they have time like.
Jose Diogo Simao: That simply says in the insight in the book, but again I want to open the discussion to everyone, of course.
Muxin Han: I think the most practical and an important aspect for for this one is he said i'm for for the politics of.
Muxin Han: causing plaques of simple model in Spain from vertex on pto with time, like with both space like tetrahedron and time like tetrahedron.
Muxin Han: there's no degenerate configuration from the from the semi classical narrative so there's no vector geometry and there's no these spirits Euclidean geometry from the rural India and.
Muxin Han: inform aptitude I think that's one of the compelling reason why we focus on the case based time like tetrahedral.
Muxin Han: And, and since we know that.
Muxin Han: The vector geometry, and this Euclidean.
Muxin Han: geometry from lauren Z and aptitude it is sometimes annoying when we when we talk about the semi classical behavior of the entire steam home empty field.
Abhay Vasant Ashtekar: right but, from this point of view, then there are pluses and minuses you know this top presented so negative or disadvantage, considering the time like surfaces so.
Muxin Han: Well, and the thing okay so so so the the the problem or here the something which which wasn't very much clear was only only appears in certain cases, or certain special cases when when when we talk about time like phases.
Muxin Han: And the advantage I just mentioned, it appears in a more generic I mean in the other case which, for example, was supposedly cancer your time like Turkey.
Muxin Han: What all phases of space like, namely and all the area operators the the usual area operated the disgrace spectrum of area operators still valid in those cases.
Muxin Han: The the the advantage I mentioned is already there, namely for when we consider you may consider time like tetrahedral with face like this the degenerate geometry is not there already.
Abhay Vasant Ashtekar: Okay, so, so what could take the point of failure that's what what you do I mean what i'm trying to say is a following even construct the quantum field theory one has a well defined.
Abhay Vasant Ashtekar: quantum theory if it is you know, once you put out or was it in the infrared regulate the whole point is how to remove it.
Abhay Vasant Ashtekar: And then one or two people don't say that a GMO any possible way they gave some orderly way to remove it, so that, finally, you get a kind of converging answer for the measure.
Abhay Vasant Ashtekar: So one could take the same point of view here right that one could take the point of view that you're saying, namely that that is our time, like the phases of space like so that in some senses, you know and then everything is okay, and that is how I should take the you know can.
Abhay Vasant Ashtekar: define the to say and you say that there is a viable idea is that machine or simoni.
Muxin Han: Yes, I think I think this is a vibe it I think well i'm from the perspective of semi classical analysis, this is.
Muxin Han: It is a consistent way to define the the model.
simone: I also like the there's something she's talking about from more maybe neighbor bonding all more genetic it point of view.
simone: Whether it's necessary or not, the one thing that may be interesting to consider is that if you want to earn or make a random sampling of a geometry.
simone: And then restricting attention to the space like once these are that we usually use, this is a very special subset because if you randomly throw points, you will get the time like phases in general.
simone: And, for instance, somebody mentioned dynamic and then you nations and they tend to use more rigorous as regular as possible.
simone: For simplicity is like a law that also which you cannot do if you restrict yourself to the old space like once, so there are some practical.
simone: reasons to be interested in continuing these extensions and it's useful to know whether the model can be defined or not.
simone: Because, for instance, for the next one that machine just mentioned it isn't clear that they have to do now is we're defining coverages and I think these results that.
simone: On one said, is about to be published to be important, because I agree that if you have a model that doesn't have a.
simone: vector geometries there might be a model that has a better behave the continuum need to be proved, but I think that's an encouraging results and.
simone: agree with a by that there's no shame in saying I should do they continue to in a specific with a specific regularization procedure not anyone, so I like that that result.
Abhay Vasant Ashtekar: that that was a case, for example in lead is he led.
Abhay Vasant Ashtekar: The.
simone: Round etc much harder to do.
Abhay Vasant Ashtekar: Exactly did he wanted to push land and random blockages and.
Abhay Vasant Ashtekar: That program basically fizzle away and nobody says anything negative about the fact that one is using very regular likenesses and.
Abhay Vasant Ashtekar: Everything that I did which sort of seems to be contributing to the logins and values aside, but you know I did this is perfectly fine and that's how they define the theory so it's it's I mean i'm not i'm agreeing with you.
Abhay Vasant Ashtekar: As technically wanting more than reality is very nice, but it does not Center okay okay well in the same bed, I just wanted to make sure that.
simone: I could see concerning these possibly the geometric interpretation of these know reggie like.
simone: But still dominant configurations prior to the branch cut hypotheses and.
simone: So we Pietro we worked out an alternative way of doing the semi classical analysis that doesn't rely so much on by vectors and it really uses the 3D geometry.
simone: And then asks the question of whether this boundary geometry defined by the golden state's can be given a flat embedding and this we're proceeding as the Nice feature that I lights the shape matching interpretation of the constraints that are needed in order to get.
simone: The southern Point two equations to be satisfied and so with that parameter ization maybe might be easier to see what concerns me seeing and.
simone: In any case, you might also be easier to see what is the dramatic interpretation of this extra piece you're seeing you may be some of what we're calling some twisting divided the shapes are not exactly matching or it might be some the answer would be.
simone: i'm on i'm just asking you, if you plan.
simone: To bring more light on the teacher.
Jose Diogo Simao: yeah I definitely I definitely have the paper you mentioned.
Jose Diogo Simao: I think i've heard a few times by now and it's it's, it is very interesting and yeah that's definitely a possibility to do, essentially the try to understand.
Jose Diogo Simao: Better recovered geometry this alternative way, which is a bit more geometric and above the twisting i'm not sure isn't it the case that.
Jose Diogo Simao: Even for the other interfaces that don't have this this problem for the other causal character choices you already have twister geometries as long as.
Jose Diogo Simao: As as soon as you can see they're more abstract train more abstractly compositions rather than just strangulations if I just have general convicts Paula he drew an abstract and arbitrary coming to 36 I already have this listing right this non shape matching at least.
Hongguang Liu: Yes.
Only.
simone: Will you call it conformance matching mm hmm.
Hongguang Liu: yeah and also I.
Hongguang Liu: know I can address the one to add something because also all these kind of geometries appear in the environment and your continuation.
Hongguang Liu: Of the screen for model and actually the equation motion were assuming that we have, so we still have this parallel transport and closure, but by the bar entered.
Hongguang Liu: By actors, do not satisfy the.
Hongguang Liu: How to see the course in physically constrained somehow yeah and also you can separate the spell actors into into the Sam or.
Hongguang Liu: Or the directors and satisfied its constituents and Cynthia you can separate eaten into two into two bad actor each director in separate into into too bad actors and then these two bathrooms are somehow.
Hongguang Liu: hi Sam geometric mean you, maybe, maybe this also also.
Hongguang Liu: have some connection with with your paper with your paper with small newspaper right.
Hongguang Liu: yeah yeah and also and also I hold down the sunglasses you know multiple, what do you see sign, I think this.
Hongguang Liu: This fixing also breaks the spreadsheet matching into into January.
Jorge Pullin: Okay Francesca has her hand up.
Francesca Vidotto: Yes, thank you again, thank you Jose presentation was really clear, I appreciated it, I had a question regarding the use of.
Francesca Vidotto: imaginary again values in the states, and so the question is twofold first of all, since we are dealing with.
Francesca Vidotto: Time like to trade right is that I should think about this as a sort of trick similar to every rotation and, if so, then your results, so, in the end of your calculate you're not really coming back to that.
Francesca Vidotto: In the sense of trying to retrieve some formulation with really embed you so so I wonder if doing such a theme may imply Australian kind of geometry, you would think.
Jose Diogo Simao: that's a very, very interesting question so Indeed it is the case that's weak reduction constructions have the disadvantage that they.
Jose Diogo Simao: constrain the puzzle the possible the causality of the space time that is recorded.
Jose Diogo Simao: And indeed, I mean, realistically speaking, if this would be constructed from a week rotation then then indeed, it could be the case that this could be some some some artifacts from that the problem is that it's a very at the very.
Jose Diogo Simao: technical level.
Jose Diogo Simao: What this is is really a technical choice, so, as I said, the way I look at it is, rather, that.
Jose Diogo Simao: We choose, we can choose any well in general, in principle, many possible basis for for studying this synthetics and some basis will be more useful than others, and I, as far as I know, and at least as far as I understand it, as far as I interpreted what we did was simply.
Jose Diogo Simao: choosing one basis that seems to be more useful and that seems to give us explicit expression.
Jose Diogo Simao: understanding it as something like a week rotation is it's a very interesting question, I do not know, I do not know.
Francesca Vidotto: it's taking the notes in it, then the corruption is a technical choice to perform an integral if it's the same kind of situation.
Jose Diogo Simao: But the point is there a true Trojan.
Francesca Vidotto: This basis and then in the end you perform the calculation and then you wanted to express your result in another business.
Jose Diogo Simao: Sorry, can you repeat that I didn't quite understand.
Francesca Vidotto: Oh, I was saying that so you perform you use this as a three and you perform your calculations and in the end of the calculation that you wanted to express the result in another business.
Jose Diogo Simao: express the resulting another basis.
Francesca Vidotto: yeah I mean unless unless you, you tell me what is the same result that if I use if I would have seen it and other business I don't see.
Jose Diogo Simao: Okay, I what I can say is that, in the original particular choice of the Caribbean states that have that have been suggested by Conrad the newbie then that were started by the way.
Jose Diogo Simao: The general structure of the functions are is essentially this.
Jose Diogo Simao: Whether whether these configurations these lights or this this know vectors appear or not in there is maybe something that needs to be discussed with me one hand I would say that I think they do.
Jose Diogo Simao: And so I would say that this is not a particular quirk of choosing a different parameter ization.
Francesca Vidotto: Okay, thank you.
Jorge Pullin: Wishing.
Muxin Han: yeah so i'm following for JESSICA question so, so I think this you complex buying Lambda is the main difference between between your work and your parameter ization and and the parameters vision.
Muxin Han: of my work with Hong Kong do so i'm wondering, so when you complex buying so i'm the about motivation or physical motivation of the company buying Lambda.
Muxin Han: So, for example, one question could be so how about area operator, so will you get some complex fight area eigenvalues from complex finding Lambda.
Muxin Han: yeah, so this is question number one, and the second question is because, when there was some work for for up i'll that and for EPI our model, it is, though, the weekly imposing including constrain it is.
Muxin Han: It is a good one, is because it says by some area matching and well area consistency condition, namely the fourth dimensional area of every operator equals two three dimensional area operator strongly you for the API on this probably less known because.
Muxin Han: Most people yeah following the paper out API Oh, and it wasn't mentioned there, so there was work and by by using and Carlo and myself and.
Muxin Han: weekly i'm studying weekly imposing the constraint using using matrix element of the operators and we find that the EPL satisfying the these area consistency condition, so when you.
Muxin Han: suppose you have the four dimensional director and the area operator and you want you want you want to make it equal to three dimensional area vector, then the model evolution yeah and until here i'm wondering suppose your complex buying Lambda then then, how do you deal with area operator.
Jose Diogo Simao: Okay, I wasn't aware of this second results of the results that he mentioned on the second part of your question, if the essential problem is this understanding of what the area operator would look like.
Muxin Han: US for that mentioned that you three that mentioned yeah.
Jose Diogo Simao: Well, the thing is that, so the honest answer is, I do not know I can speculate and what I would say, you know if you would ask.
Jose Diogo Simao: me if I would have to speculate would have to be that I don't really know what the area operator constructed on.
Jose Diogo Simao: A time like surface would look like, because the original construction is indifferent itself of the quantum gravity, which were there, you do have you start with.
Jose Diogo Simao: A globally hyperbolic manifold, so there are theories formulated on the display side hyper surfaces.
Jose Diogo Simao: And I do not know this is, and this is probably my fault, I did not know of an explicit construction or something like.
Jose Diogo Simao: An area operator or a volume operator for something like the the case that, where we are focusing on when we studied the Conrad in a bit extension.
Jose Diogo Simao: So I it's not immediately clear to me that these wonder values what's directly relates to an area, and even if they did, whether it would be you know directly, without any.
Jose Diogo Simao: multiplication by some some scaling or something by some number or whatever, so I think I think, so this is the thing I do think that this is a technical choice, I think that there is very little physical.
Jose Diogo Simao: heuristics that can be extracted from from this technical choice, but but I like it very, very well.
Muxin Han: Okay, thank you.
Jorge Pullin: So much.
simone: So we we have agreed that, having just wondering who is this who procedure, the words that's good enough let's see, let me indulge on the.
simone: idea of exploring the space of possible theories, the technical step over your construction is the fact that you can take instead of the canonical basis.
simone: These pseudo basis that looks at the little group of a space like direction the third option is to look at the note basis that.
simone: it's the little group destabilizes another direction and we started looking at these are some long time ago with meetings on Mondays and sorry and it's interesting because when you can know.
simone: Either surfaces, instead of space Lego time, like the gentleman, he is in a sense, much more.
simone: much simpler because there's a lot of direction, which is gauge, and so we only looked at the kinematic a liberal in terms of the tsp networks on analytical surface and.
simone: He looked it interesting from the point of view that the the gentleman who was delivered by less quantum labels, but we never tried to build the.
simone: screen for model out of it, and so, for the sake of exploring the the space of possible models my questions if there's anyone interested in exploring these option, which I think it.
simone: yeah sure at some point the name on and started looking at least from the customer point of view of what the simplest could look like, I think this is something that is worth.
simone: Attempting at some point, so the question is if anybody's interested in maybe you.
simone: I will be interested in helping out or just hearing the results so that's I hope somebody's interest.
Jose Diogo Simao: yeah very much I mean, of course, this is awesome sounds sounds very interesting and, yes, I would love to help out in any way, and what I can say about the know vectors.
Jose Diogo Simao: Is that when we prove mikulski serum for our to one we had to as you saw in the formulation of the theorem we had to exclude.
Jose Diogo Simao: Know vectors orthogonal to faces essentially because when you have a know hyper surface the metric the new symmetric at the hyper surface can be regenerate and then it's.
simone: boils down to political scene, so if you think about it done and now Labor surface this one direction, that is.
simone: gauge doesn't change the job because they met you guys are not direction so in a sense, all that matters is the.
simone: Is the space like to the slides so in a sense, all that matters is really also do you see, these are the level of this of the fastest speed metal is in classical version display networks.
simone: You see, that all the matters, in fact, these polygons and then, however, you extend them in another direction is just pure gauge it doesn't matter from the point of view of the geometry and so all you need are quantum numbers for this polycom so that's what i'm saying.
Jose Diogo Simao: Yes, yes, yes, that sounds very interesting, yes, we can definitely talk about this okay.
Jorge Pullin: Jonathan.
Jonathan Engle: yeah so um the way that the the the simplicity constraint is imposed in this extension of the Canadian.
Jonathan Engle: That you're there.
Jonathan Engle: minimizing this expectation value of X squared right this these generators this.
Jonathan Engle: variants of the of the generators.
Jose Diogo Simao: Let me just say that, as far as I understand it, the memorization which one is one one, it cannot be any man minimization because they're very mystics positive and negative values.
Jose Diogo Simao: But this minimization of the the expectation value of F square that you mentioned the Academy.
Jose Diogo Simao: it's not an application of the simplicity constraints it doesn't give you the simplicity constraint that particular minimization just tells you how to choose a particular reference state for the confusion states.
Jose Diogo Simao: As far as I understand, but.
Jonathan Engle: Do it does is it simplicity constraint really satisfied in matrix elements, so that.
Jonathan Engle: If you take a matrix element.
Jonathan Engle: Is it not so it's satisfied more than just an expectation value it is satisfied, but the matrix elements are vanishing Is that correct.
Jose Diogo Simao: I would have to it's possible yes, I have to go back to the original paper but yes it's possible.
Jonathan Engle: Okay, because I have some.
Jonathan Engle: Okay, because I was a I had some suspicion that if one is not really imposing the.
Jonathan Engle: The master constraint, with all positive signs, which, if you don't have all positive signs in the master constraint is not a master constraint, as you said, even classically the two constraints are not could not equivalent to each other and I.
Jonathan Engle: I mean, I have some suspicion that if you impose it that way, with the minus signs that maybe you would only get a vanishing on with with expectation values and not matrix elements, but I don't know how many.
Jonathan Engle: yeah maybe somebody else knows the answer to this isn't satisfied by expectation matrix elements are only expectation values.
Jonathan Engle: Because it could just read the paper.
simone: completely agree that the start on my circle of friends, of course, but I also don't remember.
Hongguang Liu: If I remember clearly the health metrics and.
Hongguang Liu: i'm not very bad.
Jorge Pullin: Okay, thank you.
Jorge Pullin: Any other questions.
Jorge Pullin: Okay let's thank the speaker again.
Jorge Pullin: Thank you.