On that
Eugenio Bianchi: For the invitation. Yeah, so
Eugenio Bianchi: The panel includes me Simone and Jonathan and we have the scarcity of the last weeks to try to organize something we always going to be a useful for the
Eugenio Bianchi: International community same united community. I'm going to start with a part that is
Eugenio Bianchi: That is about the symbol lipsticks and going to introduce the definitions and some of the properties and hopefully we can organize the discussion in such a way that
Eugenio Bianchi: Most of the questions can be phrased in the four more questions about single vertex questions about few vertices and questions about many vertices. And I'm going to cover these five points CI and then I leave me with to see mana.
Eugenio Bianchi: So definition of the vertex now will be brief. Take at most 10 minutes to cover this so definition of the vertex
Eugenio Bianchi: Some preliminaries Lauren's group and representations and the definition of the Y map. The thing that the PS in as a principal ingredient into the Lawrence grow into the stream from the Renaissance painful. So if you follow these points.
Eugenio Bianchi: I have festival la Uber space that carries a unitary reducible representation or the Lawrence group is labeled by
Eugenio Bianchi: real number p and an integer k and in the second line and you can see unitary video super representation service YouTube as we are familiar with labeled by Jay
Eugenio Bianchi: Now if I introduce a time like vector
Eugenio Bianchi: Team.
Eugenio Bianchi: And look at the subgroup of the Lawrence group that preserves this time like letter this defined. So one specific little group one specific issue to we've been other Lawrence group.
Eugenio Bianchi: And in particular, now I can speak about generator. So Lawrence transformations in terms of rotations that preserves these facilities factor in booths.
Eugenio Bianchi: Now in the space that carries these unitary representation of the Lawrence group, but I can introduce a basis and our normal basis that simultaneously Dahlia analyzes
Eugenio Bianchi: The two Kazimierz or the Lawrence group and then the Casimir at square one of the rotation group and alien one specific direction is it ok so we've got these
Eugenio Bianchi: Objects. Now I can define a map the wind map that sense of vector imagery
Eugenio Bianchi: In the
Eugenio Bianchi: Percentage
Eugenio Bianchi: rotation group into a vector in the representation of PK of the Lawrence group. It's a specific representation, k is equal to j MP depends on a continuous parameter gamma, which is gonna turn out to be the music Burberry misty parameter times three plus one and
Eugenio Bianchi: When, when these metals were first introduced for defining the Lawrence and spin for model the reference for us was this very complete buco rule. And now there's a primary that they
Eugenio Bianchi: Introduce really all the elements that are necessary. It is the primary by appear mafioso
Eugenio Bianchi: For in case one is not familiar with these unitary reducible representation. So the Lawrence rupa because 40 cents in quantum field theory.
Eugenio Bianchi: We learn the final dimensional representation which are not unitary, and then some infinite dimensional representation says, I don't feel space.
Eugenio Bianchi: So the simplest more familiar. Think of the sky. He is if you consider the hydrogen atom, the original trauma as a group that is larger than the rotation group.
Eugenio Bianchi: For bounced states this group is so for Euclidean group that corresponds to the presence of these additional symmetry generated by the lens vector. And so, but if you look at scattering states.
Eugenio Bianchi: These are representations of the Lawrence group.
Eugenio Bianchi: Representations of a specific kind that is very similar to the one. Consider the there's a continuous parameter analogous to gamma that tells us the impact parameter, it is continuous. Okay.
Eugenio Bianchi: So this is the mathematics behind the end I introduced already why this
Eugenio Bianchi: Is a central object. Now, the definition of the vertex in I'm referring to the angle Perera Rovelli living vertex. The Laurentian one
Eugenio Bianchi: Restricting to the case of
Eugenio Bianchi: Simply shall geometries is the one for all new pattern gravity introduced by Kaminski cielo Scandinavian dusky
Eugenio Bianchi: The ingredients at the following Tuesday graph gamma
Eugenio Bianchi: We are going to think of this graph as the
Eugenio Bianchi: Bounce that graph.
Eugenio Bianchi: Of a selling space time. So a finite
Eugenio Bianchi: Graph without boundary at this point is so we need and then
Eugenio Bianchi: As usual, to the links and the notes of the graph associates means in English whiners
Eugenio Bianchi: You use this map to inject states GM minus two states in the representation of the Lawrence group.
Eugenio Bianchi: And once you do that, the vertex amplitude is defined as in this formula. So as you see, it's similar to the expression of our speed network evaluation. There are intertwined some notes connected we
Eugenio Bianchi: Own links and object that contains the wind map contains the barbarian UFC parameter and there are integrations over the Lawrence group that make it running Lawrence invariant and
Eugenio Bianchi: One of the integral car is dropped because
Eugenio Bianchi: Via that group money for the Lawrence group is non compact and that is one region and seeing these
Eugenio Bianchi: Integrations Instagram and therefore we can fix one to one, otherwise we will get up three of divergence. So this defines completely a quantity
Eugenio Bianchi: That can be computed in fact can be computed medically and soon I will discuss many of the techniques and many of the reasons why it's important to complete it numerically.
Eugenio Bianchi: And can be studied.
Eugenio Bianchi: Analytically, and the values of assumptions have discussed briefly.
Eugenio Bianchi: Okay, point to this was just the definition of the vertex. Now what do we do with that.
Eugenio Bianchi: Well, one
Eugenio Bianchi: remark that is important is
Eugenio Bianchi: He provides a transition amplitude for Rupert and gravity states if you can team call in the following way.
Eugenio Bianchi: Choose a graph gamma in industry network, state your main choose a graph gum out
Eugenio Bianchi: In this associate is inaccurate state.
Eugenio Bianchi: Assume 40 cents, the two graphs.
Eugenio Bianchi: Coincide everywhere except in a compact region.
Eugenio Bianchi: Gamma and the elementary transition period between one state and the other is declared to be a gamma
Eugenio Bianchi: I'm not giving now the revisions. I'm stating what is the vertex now.
Eugenio Bianchi: Especially that I gave us in terms of spins and intertwine hours, but often quantum gravity, we were we were the representations for his son Solano means or
Eugenio Bianchi: Spins and normal so speed Nouriel representation or or or a morphic representation and all of these expressions are being studied and that useful in various situations.
Eugenio Bianchi: So the remark is that the boundary state space for this first X is the loop quantum gravity universe space on a graph, the one declared above
Eugenio Bianchi: The other two remarks are there is this continuous parameter that you can think of it as a coupling constant gamma
Eugenio Bianchi: These, these the Burberry music parameter in know that appears in the theater we we to independent floors in this formulation, at least.
Eugenio Bianchi: It certainly appears in the spectrum of geometric operators. Together we g and h bar always reach bar gamma and you know the place is a PR alone as, for instance, gamma plus one minus one.
Eugenio Bianchi: These are passing the dynamics. These are the
Eugenio Bianchi: parity of terms in the action at the classical level is a PR source. So in India ME, TONY I'm formulation India and the spin from vertex. You see, to. He then into these why map it contains gamma is the only object in the dynamics that contains gamma
Eugenio Bianchi: OK, so moving ahead the point three, how is this related to for the geometry.
Eugenio Bianchi: So I'm giving again the disc patronizing the previous page. We have a spin actor can transition amplitude, but now I interpret notes as quantum police
Eugenio Bianchi: By interpreting them as quantum police
Eugenio Bianchi: I can give a geometric picture and the fourth dimension of geometric picture arises. So for a sensor. The initial state. You can think of it as consisting of n in notes, each one a quantum body either on a given interval weiner. Similarly, for the out state.
Eugenio Bianchi: Now something interesting happens. So when I give the spin that we're safe with decent test whiners the factor I state of various interest whiners. This is a state of police
Eugenio Bianchi: in three dimensional space, the wine map embeds them in our forum fourth dimensional space and the by construction introduces a for vector and Polydor or leave in
Eugenio Bianchi: Three dimensional space are going to this for vector now.
Eugenio Bianchi: imposing the that
Eugenio Bianchi: The specific format of the Y map in the specific form of our gamma enters. As a consequence, the formula here in blue. That tells us that
Eugenio Bianchi: Each piece of the police later on as a three normal that slicing the plane where the police are nice and these partially fixes the map why gamma. If we impose the total matrix elements of these objects that tells us what is the normal face k minus gamma
Eugenio Bianchi: Is zero matrix elements. And we also impose that the dispersion is minimized. Then the map is completely fixed by what I declared in the first slide on the wind up. So this is one period around in 3D space if you want to change the frame you change it with a Lawrence transformation G.
Eugenio Bianchi: Lauren Symbian projection of these set of police geese, a four dimensional object it is Lawrence environment that is again the worst example shoot a note that these special as a Christian cemetery, as was originally discussed in. Yeah, yeah, one of the papers of catalog.
Eugenio Bianchi: In in the late 90s as a requirement for this versus amateurs.
Eugenio Bianchi: Okay, so this gives a geometric picture now point for
Eugenio Bianchi: There is one test that is a detailed test of the geometric properties.
Eugenio Bianchi: That I like to phrase in this form as single verse six correlations. So instead of describing the asking topics of diverse Tex. I'm telling you directly, what are the properties of correlations of the vertex
Eugenio Bianchi: Okay, so take a Laurentian vertex simply to the let's assume for simplex. This is the case, it has been a force work. It worked out in the Laurentian.
Eugenio Bianchi: Choose Aquarian binaries say they speak to a classical geometry. It's the one Laurentian for simplex look at correlations for instance area, area right angle, angle angle.
Eugenio Bianchi: In the synthetic analysis when the boundary. He speaks are now the following quantity you assume that the spin some laughs
Eugenio Bianchi: But the music parameter is sent to zero. We've areas fixed one finds it all of these correlations
Eugenio Bianchi: match exactly simply show correlation. So it could be predicted using registration gravity plus corrections over the gamma
Eugenio Bianchi: So simply show correlation sir recorders and you can associate to these four dimensional object as semi classical interpretation as a four dimensional simplex and
Eugenio Bianchi: I think also it towards in the case of a mediator. Yeah, what is the origin of the matter. Well, this is something that was
Eugenio Bianchi: That I didn't suspect we found it by the tail calculation it disparate you're the last one I could have expected and I
Eugenio Bianchi: Can tell you that the origin is the nominal GDP in the geometry that comes from vector geometry fluctuations. So this is a point to keep in mind when one speaks about the tests and rigidity and robustness of the vertex already at the level of single vertex now.
Eugenio Bianchi: I want to add one last point before closing that is the that is related to the picture of an evil vertex is related to classical theory and degrees of freedom.
Eugenio Bianchi: As you so I never spoke about taking a classical theory and quantum using it, I define the worst example to the show that satisfies a list of properties that are desirable.
Eugenio Bianchi: Now the broke picture, as I understand it, is the following.
Eugenio Bianchi: We know that if you take a topological theory of the BF kind that is a snow local degree of freedom and you can get back. General relativity
Eugenio Bianchi: If you unfreeze degrees of freedom by constraining the field everywhere in the for manifold to be a simple you get back general activity will be infinitely many degrees of freedom.
Eugenio Bianchi: What I in general I call spin forms or spin form action. Is this a similar procedure where the constraint on be is imposed only on two phases of our cellular cellular the composition of the map before this is funny number of degrees of freedom at fixed cellular the composition
Eugenio Bianchi: Therefore, the classic theory should be under control. There are various proposals for our specifically. This is
iPad di Carlo: Don't look.
Eugenio Bianchi: So there are various proposals for spin from actions classic elections, the quantization as it's funny.
Eugenio Bianchi: For a number of degrees of freedom in principle should be immediate. But the constraints that that be it make it non trivial.
Eugenio Bianchi: Party or the second classical strange Mickey material.
Eugenio Bianchi: There is a question on the other line not taking one time seeing enticing researchers ladies classical theory.
Eugenio Bianchi: Which is what has been done, especially in the
iPad di Carlo: Beginning as a
Eugenio Bianchi: Guide for finding diverse. Next, there's a different question of adding one specific proposal for the vertex in wasn't a max.
iPad di Carlo: What is a
Eugenio Bianchi: Condition on the state and on properties of this vertex amplitude. The for raw are being a spin for matching emerge and this question comes with
Eugenio Bianchi: Many sub questions and many tests already at the level of a few birds disease.
Eugenio Bianchi: For which there are specific expectations and also some concerns that
Eugenio Bianchi: Simone and john will discuss and at the level of many verse. This is where
Eugenio Bianchi: Even questions of comfortability and definition become non trivial, so I think I'll stop here and let see Mona continue. And then when there are questions I can add more
simone: Okay, let's see if I'm still able to do that procedure.
simone: Can you see my screen.
Benjamin Bahr: Yes.
simone: Okay, perfect. Thank you, gentlemen, for the introduction. In the first part. So,
simone: In my second part, I would try
simone: And then he began America results within range and vertex the extension of the analytic results missing piece or vertices and some comments on the dynamics. My slides are
simone: A bit maybe dense, but I don't plan to read through all of it. Most of the material is there just for backup. So don't get too worried about it.
simone: Sounds like to
simone: Pick it up from where a general define the model in these more general form that is a priority find on an arbitrary graph.
simone: The actual caveat there is that it is not defined an arbitrary graph completely because the interoperability, there will define us of this integral is not guaranteed for an arbitrary graph in particular, removing one
simone: Node integral is not enough. And in principle is known for a long time. So,
simone: In most of the things about general graphs that I'm interested in will concern grabs their
simone: Dual to the boundaries of politics. And in those cases, removing one result. The integration is fine it but, for instance, if you have things like a tadpole somewhere then these are these amplitude does not exist.
simone: Okay, sounds like the number three. So where do we stand with the valuation. These interior is actually even when it's fine. It is very complicated to evaluate
simone: Because these infinite dimensional madrasas here are highly oscillating and we have many onboarding integrals and we don't have that many analytic results and the metrics are really complicated. So compare these with the 15 J. The one usually deals within BF theory is
simone: An evolution point of view. One way to make progress is to use these representation theory of a cell to see, and in particular the federal data Jordan coefficients can be factors in terms of a pseudo coefficient, which introduces these
simone: Edge dipole looking like amplitude, which the Group of
simone: Students Mr say then rename the booster functions, which I think is very nice because he's the only place where a boost occurs in the range and amplitude. The rest being just an issue to
simone: Amplitude at the vertex. So these factorization here is useful for both analytical no medical investigation and has made it possible to actually compute explicitly this vertex and this is that the values applications. Let me give you some brief overview of some results for instance.
simone: If you're familiar with this dipole cosmology or Francesca Carlos jobim sale for other people. They looked at it, they had some analytic studies, but in principle, using. So these now using this increase your vertex. I'm as I said that was more or really
simone: Analyze vertex, the price.
simone: For voluntary voluntary again for volume vertices are appearing in the same form and not the fallen ones have this increase your case.
simone: So, one can actually compute numerical explicitly designed platoons and get quantitative results. So for instance, one can see that the largest been behavior of the vertex amplitude as a function of
simone: A larger spin on the boundaries. The case faster and faster as the complexity of the form increases. Maybe you could have expected. These but here, there's a quantitative statement.
simone: One can compute correlations for instance.
simone: In dipole cosmology, or people look at this diagram. Initially, it is known that the amplitude factor is is exactly. So there are no correlations between the
simone: Spins here and the spins here correlations only appear when you start something over an internal face and one can you medically compute them. See, for instance, they are positively correlated and the
simone: We
pullin: lost audio after possibly
pullin: positively correlated. I know.
simone: You lost audio. Can you hear me now. Yes.
Okay.
simone: I was saying. Another important application of these metrics concerns the bubble divergences because
simone: From the new man from the sorry analytic estimations these typically provide the lower bounds and there could be surprises there could be things that are underestimated too much.
simone: So Peter use the numerical methods are based on these approach to investigated the seven energy bubble divergence
simone: Turns out that these numerical is very complicated. I don't think is never finished this calculation numerically. But for instance. He looked at the simplified case with a full violent vertex showing that is actually convergent. In the case of the ether and model.
simone: And for these one use the some improve this estimates, which are based on the nomadic supply the just the BF theories to estimate the divergence much higher than
simone: All those the lower bound in the work he did his PhD and there's also been more interesting, very interesting also more recent work by
simone: Good genius and do not the concern evaluations with different genre Jamal then and also four dimensional BF theory more working progress that they would mention later another
simone: Well known well known. Another important application. They probably all of you already known because
simone: You have seen it or heard it presented by me or Peter or Georgia concerned the verification of the identity formula for the single for simplex which was really
simone: Tiring complicated about so very satisfactory, at least as far as Euclidean boundary data are concerned, where one gets a very nice matching
simone: That would improve the matching. You can see there's still some phase discrepancy, or we understand where that comes from.
simone: The matching the similar to the matching one gets for just us for just be BFS you to theory for the orange and boundary data, the situation is not so good. We see we can
simone: Confirm the power of decay and the fact that there is a gamma dependence on the solutions, but this is a simple formula. This is what we have in America Li is is still a long way before these actually bands enough
simone: To get closer to the expected curve, but for that one needs more powerful computer so that one can increase the cutoff in the internet sounds are pushing the speeds to higher values, something which
simone: May be possible. I just heard the from gator in Georgia, that he got access to a very powerful cluster. And so maybe we can employ some of the computing time to extend these
simone: These results here, you'll notice that in these formulas not using the original definition of the model with intertwines but the one with the
simone: With the 3D normal. So, which is the Korean birth example which boys back to this very nice work that we did, we did. There are a very long time ago. We're both still a pretty matter.
simone: And the idea is that if you are reformulate the amplitude as a linear superposition, in terms of
simone: As you do great and states, then you get this nice factorization form which you can use to start this other point analysis. So, this is the expression of the equation vertex amplitude
simone: And the boundary. Did that play an important role. So let me briefly describe them with reached from spins into
simone: The geometric interpretations, the same screen Saturday as intertwines will represent the one
simone: That usual angled incompatible with all the others, whereas these normals allow you to describe all did that. He relinquished seen data. HE DOING AND THAT'S RIGHT. THIS IS A classical feature as opposed to the intertwining one
simone: Now it is natural to classify the boundary data, according to certain subsets, for instance, one can start with arbitrary configurations or one can consider close the configurations to satisfy the crucial constraints on every node.
simone: Among the closed once one can consider those that defined the vector geometries, namely those for which the normal answer pairwise opposite are always anti pattern.
simone: And finally, one can consider data that actually satisfy the angle matching conditions on top of the pairwise opposite condition and these are equivalent to raise your data.
simone: It turns out that choosing these different sub classes of boundary data as be friend that imposes different synthetic behavior on the integral
simone: In particular, in the generic case you want to include in imposes no closure or only closure. There are no solder points and then one is an exponential fall off.
simone: In the case of Ektron geometries. One is one subtle and then there's a powerful falafel with some face. And it's important to stress that these phases arbitrary
simone: In the sense of these gauges dependent. It depends on the orientation of the normals, and not just on the shape of the data heater in the case of Reggie geometries. One is to these things. And then on top of the
Baofei Li: We lost audio again.
simone: Can you hear me.
simone: Oh,
Baofei Li: Yes. Yes, we can hear you now.
simone: I see why should I start again from
simone: What was the last thing you heard
Hal: When you started describing the Reggie case Simoni
We lost audio again.
simone: Let's see what I can try to maybe test my microphone.
pullin: Go ahead.
Yes.
simone: Where was I
Know,
simone: Back. So I wanted to stress that even though the boundary data truly three dimensionally this possible to give them a four dimensional interpretation.
simone: Because if you restrict them to satisfy the Reggie conditions than every three dimensional Reggie geometry or fake data here.
simone: Is the boundary of a flat for simplex. So, one gets a four dimensional interpretation for free is not the case for more general graphs.
simone: So moving to the next slide number seven, very briefly, why is these anti parallel condition useful because
simone: These condition of vector geometry which means that they exist rotation, such that the Normans can be put back to back.
simone: Our brewery doesn't have any intuitive a geometric media, but it turns out that he does have a very simple geometric meaning and he's the following fact
simone: That every occasion for simplex can be projected in our three in a way that it satisfies this condition.
simone: So these are special condition the capture something of the geometry of for simplicity's, however, not every such configuration of airways opposite normals comes from an op them for simplex
simone: They agreed and for simplex only spanner good you mentioned five surface which satisfies the additional angle matching conditions.
simone: This is important to justify give some dramatic picture of why these pairwise opposite condition that plays such an important role in Bartlett's analysis is actually non magical that comes from some geometric description that we know. So on slide number eight. How about the
simone: Show now.
simone: Then jack Jones very important is playing an important role for the interpretation of the geometry of speed forms and also to suggest a way to investigate the semi classical limit.
simone: It's useful to emphasize, and we have you done this with a genuine john that is not an SSRI sufficient condition.
simone: One could find ways of understanding the silica silica leave without invoking a range of behavior in the speed limit. But it's nonetheless a solid, the result also confirmed the from the aromatics.
simone: So, one can then ask the question, what is the synthetic limiter of these generalized vertices which are you all to which are not able to simply says, and this
simone: Was first
simone: And then also device then steinhauser, and more recently by the man of and they showed a couple of novelties
simone: Looking at it. Some explicit example mostly associated with a progressive disease. They showed that there could be two distinct Southern with non Reggie geometries and also show that there could be four or more interesting saddles
simone: So in our group, Mr. Say we took a systematic approach to study the syntax of these generalized vertex
simone: For months, inclusion line graphs and we confirm that these mismatch the geometries and increase the southern multiplicity an individual's genetic features.
simone: The key to achieve this result is actually to go beyond to abandon the beta reconstruction theorem and use a really, these are three dimensional geometry viewpoint that I've been insisting on
simone: And on Slide nine is a quick scan of what happens, what happens is that they can be a little
simone: More than one side or our angle matching it not cheap matching. It's only in the case of triangles that is equivalent to a ship matching. But in general, you might have conforms matches of these type
simone: And these conformity mismatch that Mr Jerome at least admit two distinct samples and it actually looks like the Reggie action in the area times for dimension of the hero angles determined from three dimensional which are well defined. Even if you don't ever energy on it.
simone: So I'm running out of time, so I cannot tell you much more free time being about the details of the structure, unless there are questions. I'll come back to it.
simone: So I would like. So just to answer it. So we know what is the syntax of these more generic vertices. And there are some surprises. They were anticipated by Benjamin and his collaborators.
simone: So now for the dynamics, which is probably the
simone: Most dedicated aspect that you have not is the head is nice green tick marks that we make questions we use, you know, I don't have one, because the question is a little bit trickier. And there's no definite answer unfortunately
simone: So if you use the screen intertwines you will recognize these as diverse example to the full partition function will look like something like this when I'm also something over the speeds in integrating over the normals that defined the Koreans intertwines
simone: This is supposed to be some quantum gravity path in a row. And so the question is whether
simone: The quantum wait at least the question for me is whether the quantum weight is dominated by configurations which are solutions of the have some classical action they correspond to democratize the GR since we are on a discrete I said in here.
simone: Two pieces of information, these financial
simone: Capital F here.
simone: To are necessary for a critical point that behavior in the autonomy to girls are the, the hero ankles. Then second America being the actual entering the speed. So if I just look at what are the configurations that
simone: Vantage the gradient of these action here. I would just get f equals zero immediately. Now I could be tempted to concluded that this means that the some sorry it is wrong. Of course, it should be.
simone: It should have been the the deficit angled should have appeared somewhere. And so instead of just did a hero angle. So if I use these two facts first that the derivative gives me the deficit angle and that
simone: That on shell of the closures angle constraints, it gives me the deputy tango.
simone: And the derivative with respect to the spin. If you vanishes tells me this function is zero and may be tempted to say that the deputy tangles would necessarily be zero.
simone: Which will be bad because then there's no curvature. There's no interesting dynamics in the model, but these argument is wrong.
simone: Because everyone zero is obtainable vanishing respect to the scenes, but f coincides with the deficit angle only if they spent a normal are constrained. And then I cannot do this variation with independent spins.
simone: So I'm more precise analysis is required to see what the dynamics is really like. And to understand these my best intuition is the one that they got from it and go, Reggie calculus.
simone: Because let's not forget that we're getting is not just directly in action in terms of the elements as it is, Reggie calculus.
simone: Or rather, in action in terms of areas and the usual angles, which are defined by this killer products from the 3D normals. And what will surely blank, a long time ago was that these type of structure that arises at the synthetics is consistent with a
simone: new a new
simone: Question is,
simone: Actually a nice and simple calculus. It's equations emotions are a bit of a mess. In particular, if you look at the variation respect to the spin
simone: We get a deputy dangle as I should have written around instead of the, the hero, Michael. Sorry about that. But that's a contribution that comes from these plugins, you multiply your meal.
simone: If I forget about these again of course flatness, but these contribution is there and this becomes equivalent to their education. Only once they've sold all of the equations. He particular also THOSE THE FIX THE LUGGAGE multiplier.
simone: Now the structure of it encourages you to set the structure just described. There's always made me might be optimistic about the fact that the patron model may work.
simone: Because if I interpreted as the exponential of the rejection as bad as as the ride time some delta functions that impose the closure and she matching constraints, then we're looking pretty good.
simone: And if I will get pretty good, then we can move to the really interesting questions which is not just to get the Reggie behavior, but to see about quantum corrections.
simone: However, and I moved to slide 13. This is actually a very fragile structure because if you drop these new term here, you get immediate you lose different solutions and if you
simone: Don't know what is exactly shape or because actually it is not a delta function, but it's some type of GAO Xiang and maybe it's abroad Gershon
simone: They were not looking very good. Then we are losing the prevalence with Reggie calculus and we are losing possibly called the solutions as well.
simone: So that's for me the way of looking at this problem. I never quite succeeded to get these in concrete answer.
simone: On the content most investigations along the years I found that no evidence of this etc and concluded that the model is only for distributions.
simone: And now I personally have technical counter arguments to every of these technical analysis, but don't find it very useful to go into the details here because you would think.
simone: And because they're very technical and it's easy to not agree. Easy. So instead of like to
simone: Consume suggest an alternative which is forget about fighting or a technical details let just let the medical check
simone: And a very simple test ground which has already been discussed in the past is delta three triangulation, which has three four simply says sharing one face. Now this is not the ideal setting.
simone: Because even though there are internal degrees of freedom being some Dominus painful model, the internal face and also the intertwines here.
simone: From the point of view of Reggie calculus. There's no dynamics here because all the edges are boundary edges.
simone: Steel at one can cook up some trivial test, which is to ask that all the boundary data are such that the edge lens are fixed to be either those compatible with curvature or without curvature at these internal internal face and then one can study where whether this been phone and
simone: Internet speed. The one is coming over on the one that is compatible with their edge interpretation or not. These are not to be a non trivial test.
simone: And by not your test. I mean that if you run this test will be f theory, we have to actually fields, it
simone: In the sense that if you choose the boundary data so that the spin should be flat.
simone: Then you get a stationary point for that flat spin. But if you fix the boundary data so that there is curvature, then
simone: There is no stationary face or the spin correspondent for with this curvature solution. And this has been recently beautifully shown by Peter in Georgia with dental medical code and I hope they will
simone: Publish it soon and then move on to the business case, which is what we're interested in the most and hopefully give us a clear answer by the summer.
simone: By the end of the summer, maybe, hopefully. So to summarize, and so if I run or have run over my time. I think that we, these rights and MP to these
simone: Something that we can very well compute with
simone: My main advice is to use the same routine.
simone: And there's lots of work that one can do and at least at some valid point of the work that I would like to see done in the upcoming time
simone: There's hundreds of different signature vertices is also known, of course, there's, there's an issue whether one is really interested in these generalized more than
simone: Or whether one would like to be something tighter somebody that is closer to having only Reggie geometries in the semi classical limit.
simone: And so to modify the model in such a way, and they know the Benjamin, or at least by the bell on the student have been working on this.
simone: As far as the dynamics, the situation is more open for discussions and I've given my advice in my bullet point here and maybe we can come back to it, and I should pass it on to john and sorry again for running too late.
FAU: Okay, alright, just let me
FAU: Do you see the slide is that, am I sharing successfully. Yes. Okay, go.
FAU: Part of the
FAU: Of the panel. I'm going to be talking about these debates on
FAU: Degenerate sectors and the cosine issue and the, the so called flatness problem. Some only talked about this a little bit at the end of his part.
FAU: So, and
FAU: I'm starting with the quantization, which is leading to the PRL model so that one can really starts from the the BF vertex amplitude
FAU: And here I've represented the the boundary state as a coherent state I'm emphasizing that this is a state in the boundary Hilbert space that's peaked on certain values of the discrete be field which is like a discrete polonsky field, these, these by vectors and and the y map as
FAU: As Eugenio reviewed embeds su to representations into SL to see representations, but those can be assembled.
FAU: Into a map from the SU to boundary Hilbert space to the SLC boundary Hilbert space and then the parallel amplitude is just you just take the the SU to loop quantum gravity boundary
FAU: State and you just use the Y map to map it into a an SL to see boundary state and just plug it into the BF amplitude. So it's really coming from
FAU: Obtaining gravity as a constraint BF theory.
FAU: And and so what I want to do is I want to
FAU: Look at the the awesome topics of the of the parallel vertex and understand the geometrical meaning of the critical points that are appearing in the SM tonics by reconstructing the the continuum pull up polonsky to form which will then allow you to reconstruct a continuum.
FAU: tetrad a foreman, and then we can see what how do we interpret these critical points is degenerate versus
FAU: non degenerate and which ones have positive negative orientation. So the meaning of the of the group elements in the group integration is really parallel transports
FAU: From we think of it as from a tetrahedron frame to the force simplex frame. And so in order to assemble the by vectors into a continuum to from, we first have to parallel transport them all to the same frame with the with the group elements and then
FAU: As long as the, the critical point equations are satisfied, there exists a unique to form on the floor simplex considered as a manifold.
FAU: Such that the by vectors are just the integrals of this to form.
FAU: Now there's a caveat here. This is really only true for the for simplex case. But the general for cell case the accounting doesn't work. And so in general, it's not guaranteed that the that the to form will exist, but so I'm focusing on the simply showcase for this part of the talk.
FAU: So I'm
FAU: Yes, so
FAU: The two forms so constructed
FAU: is either going to be of the duel a wedgie form. So the here I the be I'm using here was actually the the dual what Eugenio used
FAU: And in that case, you have a tetrad which has an orientation.
FAU: Or the other possibility is that the the to form is degenerate. So I'm denoting these these cases with a sign omega which defined to be zero. In the degenerate case. And so this table summarizes the the different critical points and
FAU: Which sector, the continuum be falls into it for these different critical points. So in the case of boundary data that fits a Lorenz Ian for simplex
FAU: You have to critical points, corresponding to each of the I read J action and each of the minus i read J action and these corresponds to two different orientations of the tetrad
FAU: There you have a non degenerate tetrad in that case. In the case where it fits a Euclidean for simplex. Actually, what you get is a is a degenerate to form.
FAU: Which is a little bit
FAU: Not intuitive because it would seem that if it fits onto a Euclidean for simplex it's it's not degenerate. But as someone he was pointing out, you can fit together.
FAU: If you can fit together and tetrahedral onto a Euclidean for some flex and you can also fit them together in a flat three plane which is really what's happening here. So these are all degenerate and mission introduce this terminology degenerate type eight degenerate type be
FAU: At someone is request I introduced this first column here it gives another way to understand whether these boundary data corresponds to
FAU: non degenerate or or degenerate for simplicity's using the Kaylee for volume, which as you can see, doesn't really doesn't necessarily fit the categorization here. So there's another way to understand whether these
FAU: Boundary data are degenerate or not, but here I'm I'm focusing on an interpretation which comes from the quantization.
FAU: And the interpreter and the
FAU: Classical correspondence with the discrete variables.
FAU: And the other cases, of course, the vector geometry.
FAU: Let me go back. So that, so the cosine. Problem is, is the is the fact that we're sending over orientations here that you can have both possible orientations and the large spin limit. And then of course we have all these the degenerate sectors and
FAU: The degenerate sectors clearly are not corresponding to something which is gravitational and then there's some debate about whether we should have a be something over orientations.
FAU: The awesome topics can be extended to a general triangulation, which was done by
FAU: Han and Zang. And so what you get is basically you have a some over all possible
FAU: Of these sectors it for each of the for simplicity's independently. So you have a region where it's not degenerate, a region where it's type a degenerate in the region where it's tight be degenerate and within these regions you. Additionally, some over
FAU: Orientations so um so the action that appearing in these topics, if we if we multiply them out, then you
FAU: Then you end up getting an action for the whole amplitude, which involves a sum of all of these actions with signs depending on
FAU: The floor simplex. And this is clearly not the rejection in order to get the red Jay action we would need to not have any degenerate configurations and restrict ourselves to a single orientation or at least not allow the orientation to change.
FAU: And so if we're hoping to obtain gravity by looking at the large spin limit and
FAU: Hoping that the stationary points of that larger than limit or what's going to dominate the path in a row. This is not looking hopeful.
FAU: Because the equations of motion determined by this action or not the equations of motion. And so you're going to have more than just Reggie geometries dominating in the in the large spin limit and
FAU: So you're going to have knowledge of geometry which are which are co dominating which are just as just as as persistent as the equation. So it's not clear that you're really going to get the right
FAU: Some classical limit. And furthermore, these non Reggie configurations are
FAU: suspected to be the source of divergences
FAU: But to understand why the why the these, um, there's some over these different sectors is expected to lead to the divergences it's, there's this work done by
FAU: By Mario's and and others, a while ago looking at the ones on a Reggie model. And there you also have some over orientations for each simplex or neck case there tetrahedral.
FAU: And what you get, again, is an action where
FAU: You have some over lots of different actions where
FAU: The sign is allowed to vary from tetrahedron to tetrahedron. And what this leads to is equations of motion that is not flatness which which which is what you should get into plus one gravity, but a sort of oriented flatness so
FAU: If you define the deficit angle by
FAU: By
FAU: summing over the digital angles weighted with the orientation, then this is what is I should have said this is a two pi, not zero.
FAU: So it's not quite flatness it's some oriented plans. But the point is that this oriented flatness is not the same as flatness because this oriented deficit angle is not deficit angle and a very easy way to see that is that such geometries cannot be symmetrically embedded into our three
FAU: And
FAU: The fact that these configurations can be distinguished from actual flat configurations was pointed out before by these same authors.
FAU: You can see what what what what sort of configurations are allowed. So on the left here, we have
FAU: A flat configuration here I'm visualizing in two dimensions, because it's easier to visualize what's happening, two dimensions.
FAU: And around this hinge. You have no deficit angle. But then as soon as I move this central point outside of the triangle, we have a pocket or a spike and the the
FAU: You have curvature then around the hinge, even though it looks like it's flat, it's not really flat, it's not you have a pocket in there that's not embeddable into a
FAU: Fund space.
FAU: And so the idea is that because these critical configurations are allowed.
FAU: This is actually what's leading to the divergences that appear in the puns on original model because if you just consider for example this
FAU: This this tetrahedron that's been sub divided into four tetrahedral and
FAU: In the, in the path integral, you're going to effectively you're gonna end up integrating over
FAU: The possible positions of this internal vertex and if if you if you really only had the flat configurations which were dominating. This would be a compact integral and you'd
FAU: You'd expect not to have divergences but the point is that because you are allowing these other orientations and these non Reggie configurations. The you, you also have to consider the case where you have the pockets and this. So the central point
FAU: Is gives a critical configuration, no matter where it's placed outside or inside the tetrahedron. So you end up with a divergent integral. And the idea is that this, this can be understood as as the as the source of the divergence is in the hands on original model.
FAU: Another interesting question is, if it's really physical to be something over the orientations, you know and and you there experimentally distinguishable, why haven't we seen any such effects in particle physics experiments.
FAU: Because really it's not just fluctuations that would, that the model would be predicting it would be predicting that these are co dominant contributions to the pathological
FAU: So, yet the dancehall reggae model. It is triangulation independent after regularization, so it seems to be, which is a good indication that it is a correct model of topological theory, like, two plus one gravity, but is it really two plus one gravity. I'm not entirely sure.
FAU: And of course the
FAU: The parallel model has the same issues which you will you will you will only see it for for multiple simplest these these problems arise, but one possible solution that
FAU: I am collaborators proposed some several years ago is the proper vertex, where basically we insert a projector which projects onto the single orientation.
FAU: And enforces a single
FAU: Enforced is not degeneracy with a single orientation and the advantages of this is that
FAU: You no longer have some over orientations.
FAU: All the degenerate configurations are suppressed and so you don't expect the pockets of the spikes. And so, the expectation is that the divergence is will be reduced. You can define it for both Euclidean and Lorenzo and signatures and so far.
FAU: It has the same successful consistency checks and applications to grab the grab on propagator and spend phone cosmology of one major disadvantages that right now. It's only restricted to some initial triangulation.
FAU: It's, it's more complicated than the PR L model so that some
FAU: Some more innovations would be necessary to really do numerical calculations and also
FAU: There's an ambiguity in the definition because you have a choice of where you can insert this projector that's projecting on this one sector, you can insert it at any of the tetrahedron. So what we do is we just
FAU: Insert it in all of the tetrahedron, which one could argue is a bit ad hoc and suggest that maybe there's a there's a better way to do it.
FAU: which avoids that and perhaps even simpler. So what I want to say is that is the proper vertex is is not necessarily the solution, but it's at least a solution to the problem of the some over orientations and and the degenerate sectors.
FAU: And I want to emphasize that. I think it is a. These are problems which needs to be solved. And we will see these problems when we do calculations with multiple for simplicity's
FAU: Another, just to clarify some things about this.
FAU: This idea of restricting to a single orientation was suggested a while ago, in the context of the the Barrett crane model by in this paper by Levine and Ricci
FAU: And
FAU: And they really suggested that
FAU: That if you if you restrict to a single orientation. What you're really defining as a as a causal propagator which is analogous to the fireman propagator and and that actually, in such a case, you don't expect it to.
FAU: To satisfy the equations of motion. So in this sense, you don't expect it to give a
FAU: A projection into solutions to the Hamiltonian constraint, if you restrict to a single orientation.
FAU: But their, their viewpoint, was that both of whether you restrict to a single orientation or not. Both of those possibilities would be useful for different purposes.
FAU: But I wanted to emphasize that in the limiting the sum of orientations. It's much more than just imposing causality. You're not just enforcing that the final state be in the future of the of the past state. There's you're eliminating all these spikes and pockets, which don't
FAU: don't correspond to anything that we see in classical gravity and also there's other work, which suggests that maybe the the
FAU: This something over the orientations is not needed in order to get a projection and solutions and Hamiltonian constraint. In fact, this paper by by Thomas and Antonia actually suggests that
FAU: You need to get rid of the some over orientations, in order to to get a projector into the Hamiltonian constraint. Also in this old work by
FAU: By hurdle and hawking on the no boundary proposal. They're integrating overall Euclidean geometry. So there's no there's no some of our orientations there but yet they still get
FAU: solution. The solution to at least a formal solution to the Hamiltonian constraint.
FAU: So this summer is that of this issue is that there tends to be consensus that the degenerate configurations are problem and are contributing to two divergences but there's
FAU: There isn't consensus from what I find talking to people that the elimination of the cosine
FAU: Is the physical correct thing to do, it does when I do talk to people that there is consensus that elimination of the cosine is likely to reduce divergences it's just not not everyone agrees. If it's the physically correct thing to do.
FAU: And the proper verse vertex eliminates both of these issues above
FAU: But it doesn't mean it's it's the only solution or the best solution, but it's it's the only solution. So, so far.
FAU: So finally I just wanted to make some clarifying remarks on the flatness problem so morning already said some things about this. Here's a brief history of the flatness problem. It was first noticed by Conrad infidel and buns on
FAU: And
FAU: Later.
FAU: Both in near about the same time motion Han and Frank Hellman and what tech Kaminski found that if you're more careful you don't quite get flatness, but you get an accidental curvature constraint. So the gamma times the
FAU: Deficit
FAU: Angle it should be zero module for pie and Hellman and comin comin CD got that it should be modular to pilot, but quite sure what explains the difference of the factor of two. There
FAU: And it should be emphasized that mission pointed out that he didn't. He didn't see this as a problem that actually the deficit angles should be close to zero and the refinement limit. So there's some question about whether
FAU: You know, even if flat configurations do dominate and large spin limit whether, whether that's a problem because maybe the large spin limit is not the right way to
FAU: Consider the semi classical limit.
FAU: There was so all of these were arguing in favor and some sort of flatness, there's another line of argument which tried to show that there was no flatness and
FAU: Which started off with Elena and cloudy. Oh, and 2011 they're the first ones I'm aware of to to use this delta three triangulation.
FAU: To to investigate this question to make concluded that
FAU: That it allows internal curvature, which is not suppressed. But more recently Olivera given more precise version of their argument.
FAU: And the key thing is that it really treating those some over the internal spin something over the internal spin and keeping it
FAU: Discreet not approximating it as continuous. However, there's an oversight, which when correct it actually provides a new argument for that accidental curvature constraint. So this is unpublished
FAU: I mean I guess I shouldn't go into the details, but basically, let me just say that there was
FAU: That there was this imaginary part of the action which Olivera had neglected and when you when you don't neglect it. You, you actually end up getting a the same accidental curvature constraint as as motion haunted and almost telman Kaminski modular this factor of two issue.
FAU: So, but the weaknesses of the of this argument.
FAU: This modified Olivera argument is that first one is taking the large spend some time limit, and then something over internal j is not clear. If this is correct. Also, one is neglecting the dependence of the SEM factor on the internal spin
FAU: And Simone a pointed out that in part of this derivation. One thing that's key to this derivation is is approximating the amplitude in the neighborhood of the critical points.
FAU: The critical points with respect to the the continuous variables. And when you when you when you look at the amplitude and then in the neighborhood. You don't see any evidence of imposition of the closure constraint and shape matching constraints. So
FAU: Which indicates that perhaps these these holes in the arguments are causing the, the key point to be missed the thing which could save you from the flatness of we're not seeing it.
FAU: Perhaps because of these proclamations so so my summary of the of the status of the flatness problem is that every analytical arguments so far. When sufficiently refined
FAU: Yields and XML curvature constraint. However, all of these analytical analytical arguments either have clear holes are are difficult to understand. I haven't wrap my mind around the way front.
FAU: Analysis of filming Kaminski and
FAU: So I really think that the flatness issue is really only going to be settled with numerical calculations and so I'm really excited by all of the
FAU: All the numerical work that's being done in my say. And so I'm hoping that this flatness
FAU: Issue can be settled finally
FAU: And another remark is that even if you do have such a curvature constraint. It doesn't necessarily mean the model is incorrect. But perhaps the semi classical limit needs to include a limit of refinement and which actually deficit angle should approaches you
FAU: And that's
FAU: That's all I had the remark on those issues.
FAU: So I guess we're open for general discussion now in questions.
simone: I think there will be good.
Yes.
simone: For this plenty of topics in
simone: The context of spin for models that we haven't really covered in our presentation. So it's also time for other people to comment.
iPad di Carlo: This is a, this is Carlo can, can you hear me.
simone: Yes.
iPad di Carlo: Okay.
iPad di Carlo: I just want to make a small
iPad di Carlo: Observation is say it's not directly related but it's related to what all you, all you have said this is something that has been new for me. It comes from the numerical calculations.
iPad di Carlo: And I just want to share it. And is this. Um, I've been trying to use the this
iPad di Carlo: Current formulation for doing
iPad di Carlo: Physical calculations in black holes and cosmology and in both cases, it's
iPad di Carlo: You can view it as tried to compute tunneling aptitudes, whether from the contract the universe to expand the universe or from nothing to universal from a black hole tobacco and Francesca Tina has been doing some numerical calculations in for early cosmology and
iPad di Carlo: He has found some some nice expressions that that's not the point. The point is that by looking at the metrics will turn out to be relevant seems to be not the lorente and Reggie geometry. So, but
iPad di Carlo: Some Euclidean so some better job, which is in facts in in in detailing. So this is, this seems to be coming from the numerical. So what I want to say is that, perhaps, of course, quantum mechanics should give us more than the classical limit and
iPad di Carlo: One way of viewing tunneling is that that path integral has some not really subtle points, but some Euclidean subtle, subtle point some some some somewhere else.
iPad di Carlo: That waits into some at any sort of tempting to imagine that this other
iPad di Carlo: The bushes to the amplitude do play a role in the quantum theory and they do play a role in in tunneling. So it might be
iPad di Carlo: That
iPad di Carlo: The quantum theory.
iPad di Carlo: That we have is, is it is Mark is marked. What I'm suggesting is just not let's not just be for opposite to the fact that
iPad di Carlo: In the past will all the classical configuration should come out. In fact, it shouldn't be like that because quantum theory admit tunneling.
iPad di Carlo: This is not a precise point. But I think is an interesting point to keep in mind.
simone: So we haven't yet established at the same classical limit is correct. And there is a risk that the sector vector geometries may cause problems with regards to that.
simone: If it does, then the fact that the sector of actor geometries give some interesting contributions to tunneling, and maybe less relevant so
simone: It's a very nice that they can give some interesting contribution that sense, but we need to make sure that they don't spoil the semi classical limit, I suppose. And then we are free to emphasize these results and like the applications even more I'd see
Eugenio Bianchi: So what
Penn State: One of the reasons why this, we had this panel was because there was
Penn State: No, people are asking kind of rather elementary questions. And so I would like to go back to those elementary questions and I want to thank especially Jonathan more making a nice list of those questions and those questions were a sort of semi classical limit be a flatness problem.
Penn State: And
Penn State: See the issues of divergences and I think
Penn State: Usually a girl very general, you know, all picture, but somehow I didn't see these these problems being directly
Penn State: Answer there and SIMONE IS TALK. I got the impression. And so this is what I want to understand Simone and Eugenio and Jonathan please correct me because we just want to be all on this similar wavelength, even though we may not all understand the technical details.
Penn State: So I got the impression that the issue of divergences is still open and sort of looked at and, in particular, the focus in the numerical simulations, which is very, very valuable.
Penn State: Has been really just restricting was after cases where diversions don't occur. So this point number one. Please afterwards comment on this point number one.
Penn State: And number two, that flat. This problem is still open the arguments, saying that it is flat, but there are wholesome those arguments.
Penn State: And again, Simone and and Jonathan emphasize that. But as what we need is really this numerical simulations, but I'm a little bit confused because I thought that numerical simulations. So far, I mean,
Penn State: There were being performed is restricted context. And I'm not sure that in the near future. I mean, I'm the time scale of a year.
Penn State: That the numerical calculations will be done in the context, which covers all these reservations about the flatness problem. So I would like answer to kind of
Penn State: This thing to do. Second question. And the third question was about this orientation and cosine problem and I mean this has been all these three questions I've been raised by many people. Many times, and I
Penn State: I get I got the impression from Jonathan stock that
Penn State: Unless one really sort of my hand, the requirement that one should just some or one orientation than this problem is there and
Penn State: And more importantly, I felt that he was emphasizing this missions point of view that somehow taking large Jay is not the correct way to take semi classical limit.
Penn State: Now usually emphasize that taking large Jay and resetting gamma to zero size that data and the gamma is finite. Maybe the appropriate way of taking the classical limit.
Penn State: I just let me open a small balances. I think all this discussion is much more much clearer if instead of gamma when he uses the gap.
Penn State: Think of area gap as being independent of GH Barbara plan, plan, so to say. And in other words, if you like the numerical coefficient of the gap. And so what what you're saying is that we've we've sort of lead.
Penn State: Area gap, go to zero j goes to infinity, says the data is finite, but then usually pointed out that there are corrections or daughter of gamma, which is to say correction, daughter of area gap and so quantum geometry which leaves you outside the
Penn State: Other thing. So I'd like to get clarification on all of these three points from the three speakers, because I think it's not just for me. But for many younger people who are asking similar questions.
Penn State: So on the point of flatness, it seems to me there are lots of ideas in a partial proofs on the analytical side. And I understand that this might be feasible, at least, using the data reconfiguration we've been
Penn State: One, maybe two years, one could answer that completely by using metrics.
That requires the definition of what is the problem that is worth formulated even numerically. So in our discussions with john and see Mona. I was proposing something of the kind, because the, the critical point is the flatness award connection or what controversially Sita
Penn State: Spin connection. Is it the actual connection. I see the levee Shibata connection. So one thing that I was proposing is to look for a sunset.
Penn State: For volume in the boundary three volume and defining geometric core machine in those terms one fixes the boundary and then compute the expected value. The for volume. This will give a test of flatness, but they will send the sun is difficult to use know medically
Penn State: The other mark is that
Penn State: Question. So this kind like flatness can be phrased using only few verse disease is factors can be addressed directly numerically. There are other questions, like the one of divergences that they would appear once when, as Steve few, but more vertices at the level of a bubble
Penn State: So there are necessarily one as to truncate the some of the speeds.
Penn State: Either we have a quantum the formation or by and by putting a cutoff and
Penn State: So that makes the medics difficult if one was to see their dependence on our this cut office remote on the other end, if we want to go too many vertices and start testing the behavior of
Penn State: The spin for model we many varieties is to ask all the questions, it seems to me a reason a bola to start looking at locations where the truncation spins is not large.
Penn State: But smaller, possibly as small as he can get for instance only spin 01 alpha where the vertex is purely quantum in the sense of one is not taking any limit.
Penn State: At the level of the single worst x ray starting to ask questions that are genuine genuinely many, many body questions and
Penn State: We have been working on this with Pietro we have a formulation, where are these truncation has done consistently by promoting the Masonic representation representation which gives again.
Penn State: Quantum group the formation as now lambda is not being understood as a cosmological constant something that has to be smaller.
Penn State: Or larger solution scale but campaigns clunky and object. So I think, I think.
Penn State: I think
Penn State: This is something could be explored dramatically and some of the questions are too many businesses. So the second part that you just mentioned.
Penn State: Is it possible that one girl. So look at this many, many words is with small jays to also look at the classical limit question or is that something that for which you you think that large Jesus and James gamma fixed is only way to do it.
Penn State: I think that many vertices. So it's more spins something I want can use us to test the semi classical limit 40 cents in the version where one looks at playing functions of fixed distance. It's boundary distance and from the top and functional one tries to derive an effective action.
Penn State: The value of taking one single verse text and sending it to infinity. I find it still plays an important role because
Penn State: Even when we study spin systems even enough many buddy feces when one study spin system see some valuable to do this.
Penn State: rescaling where what each one of the spins vas has a classical vector and when as a model of the many buddy system.
Penn State: Where each single spin is risky as if it was legit. So I think that there are aspects that there are things that we are learned and we might keep on learning by studying the specific limit. But I don't expect this to be necessary for finding the semi classical Fujimoto
simone: Maybe quickly. Yes. So concerning the first question of a by on the divergence is yes, they can be investigated numerically. It's hard.
simone: The first one that appears as he was shown is my slide is the bubble divergence with to the self energy to for simply says, I don't know. Maybe Peter wants to comment about the feasibility of doing that in the upcoming months.
simone: But yes, you can maybe see the new medically the flatness also as a junior say the delta three is undergoing
simone: Larger strangulations with internal edges as I was mentioning would be the next step that may require one of these super clusters and maybe hopefully we can get access to it.
simone: I as for the semi classical limited there's something that maybe people are forgetting. But these Reggie behavior. Let's not forget it appears of speeds over there 10 to 50 the Laurentian as in politics around somebody did is the worst case he will probably appear 50 to 100
simone: So we're talking about being at
simone: 50 or 100 times the planck length. So it's hard to criticize these as being a gigantic for simplex. So these are edge behavior appears extremely soon.
simone: And considering the same issue. I think the best thing to say is that there really is no consensus.
simone: Even john new genuine myself, even though they do many things on the issue because I don't think we have any clear view in. So I think that's part of the we need more results within more results to get consensus there. That's my view.
Penn State: Thank you very much, so on. So just, again, I just very naive level that particular students and postdocs keep asking if there are, I mean you could
Penn State: Try to calculate those divergent diagrams numerically, but the statement is that they are divergent right and so just calculating the coefficient or something like that numerically. And the question is really values divergent diagrams, then what is our view.
Penn State: Is that we just keep them. What, what, what, what is the point.
iPad di Carlo: Can I, can I comment on this says please
iPad di Carlo: You asked about this three three issues. So let me just give what is, what is the viewpoint about this distribution. So let me briefly summarize the my viewpoint of the three issues. First of all,
iPad di Carlo: The divergence is the the state of the of the theory is that the theorems in which there are no divergences
iPad di Carlo: The several for the version, the quantum deformed version which is much harder to compute with and which has a cut off.
iPad di Carlo: An infrared cut off, which can be interpreted as a cosmological constant. So we always knew that without that
iPad di Carlo: Without that there are these infrared divergences
iPad di Carlo: How do they come in.
iPad di Carlo: In a trap acquisition. How do they wait. I think it's all will be explored and whether they need
iPad di Carlo: They need to grow into my eyes away or whatever. I think I don't have clear ideas. I don't know if anybody else's gear ideas, um,
iPad di Carlo: My hope was that there's a number of things that can be computed the
iPad di Carlo: Like in in quantum field theory before actually going to terms with this infrared divergences come in and this would give us a hint, whether the theories. Interesting.
iPad di Carlo: Already, um, then to address it was just one of the two either the virtual with a quantum group is we're actually what has to go.
iPad di Carlo: Not that the solve the problem. But this at least give us theorems that things are fine it or they have to be normalized in some way. And this is my opinion is open.
iPad di Carlo: And regarding the flatness
iPad di Carlo: Issue.
iPad di Carlo: I am not convinced by these analytical results I find them.
iPad di Carlo: Incomplete and they all seem to miss the
iPad di Carlo: The key detail that intuitively seem to
iPad di Carlo: Suggest that
iPad di Carlo: There's a reason for this to be to be flat. So since I'm anything is complicated. Since the sweetness of jays crucial in this in this sort
iPad di Carlo: What intuitively, what matters is how large is the
iPad di Carlo: How, how large is the bump of the
iPad di Carlo: Around the subtle point because it is really an issue of exchange of limits the limits in which we restrict the integral around the subtle point
iPad di Carlo: Versus the signature itself so
iPad di Carlo: I analytical I'm not able to to give an argument solid argument that make the intuition that this is to be
iPad di Carlo: We try. We have tried to do the numerical calculation in in in in Mercedes since we've tried with this stuff. Seven years ago,
iPad di Carlo: Still with Francois
iPad di Carlo: I think we're moving toward that. And I hope this is a very good nice problem it's it's relatively clear
iPad di Carlo: And it will be solved, and I agree with Daniel that once you be careful in interpreting things and asked, What exactly
iPad di Carlo: Are we asking to the theory, we might be confused. The interpreting this data us curvature that might be one of the sources of the of the question. So the real question here is whether we get the classical limits. Correct.
iPad di Carlo: In a situation in which there is a too complex where we expect to be curvature inside so
iPad di Carlo: Let's
iPad di Carlo: address the question halfway through this is the right question. And I think it will be solved with sufficient effort. The third question is about the cosine
iPad di Carlo: I agree there's no consensus there. There's definitely a positive always be no consensus, I expect
iPad di Carlo: The, the, the, the, the amplitude to have both terms.
iPad di Carlo: I think it has to have both terms because the winner. David equation is real, because that would be expect from the theory. This is not defined by the exponential of the
iPad di Carlo: Of the
iPad di Carlo: AI the classical option.
iPad di Carlo: These are just type. What is it I find an eight arguments like oh, but then we should see physically
iPad di Carlo: Some physical effect of the other term.
iPad di Carlo: Tweet.
iPad di Carlo: And not not found it. I think that OTT and even had a point is saying the quantities in in in fuel theory, though, to kind of propagate those one that propagates ahead and went propagates ahead and back.
iPad di Carlo: The the the
iPad di Carlo: Spin form includes
iPad di Carlo: Both of them. Now let me be clear, this is not a reason for thinking that what john does is not interesting mainly his considerations are interesting.
iPad di Carlo: As a motivation to explore something else as a motivation to expose anything else. Very well. So if there's another theory.
iPad di Carlo: With a proper vertex that works fantastic but they don't think their motivations are strong enough to doubt that without it, it might be, it might give them the classical limit. Correct. Nevertheless,
iPad di Carlo: So I worry much more for how we will be able to control the divergences
iPad di Carlo: And
iPad di Carlo: How this will affect calculations.
iPad di Carlo: Then
iPad di Carlo: Then a priori arguments, this should be wrong. And I think that this is going to be tested by using this, not by keep going around in a circle on on abstract arguments. So once we can compute something suddenly things will become much more clear.
Penn State: That's it. Okay, thank you very much and I can know that that was very helpful. There are people in API, who I think are strong views about
Penn State: The issues and limitations and I hope that they can speak up so that I think everybody kind of comes to the same on the same wavelength. Can people in ti please pick up
Marseille: While we wait for people to wrap up their mind if they want to intervene. Maybe I can address
Marseille: A couple of points in response to a bias question and try to specify a little bit more what Simoni was saying. So about the nomadic so in particular.
Marseille: The nomadic say
Marseille: We have a code that works very well for one vertex diagram the code works also for
Marseille: Two or three vertices diagrams in particular.
Marseille: divergences as being computed the within BF beauty and
simone: Center. Once they got john, can you stop sharing the screen so I can show the vertex diagram that Peter is talking about. Go ahead, Peter. Sorry. So
Marseille: The vertices has been completed numerically for BST.
Marseille: In three and four dimension by three and four dimension. I mean, using vertices that are four and five, Ireland and they both the verge as they should be, because the computation can be also done analytically. Exactly. Then the computation of the agencies that I perform the
Marseille: Art regarding the diagram on the left, so it's our if you wanted some time or the for the epl
Full
Purity
Marseille: Where they just so they're the group is a sad to see. So it's burdensome. But then restricting to football in vertices. And for those kind of
Marseille: Theory, I was able to complete that diagram and that diagram is not divergent
Marseille: What but
Marseille: Then for the full four dimensional theory. The one on the right.
Marseille: Was not able to perform the numerical evaluation, but I was able to use nomadic estimate
Marseille: Our love for the single components forming their the amplitude and there was able to estimate the divergence of the diagram but just growing together informations
Marseille: So I don't have numerical computation of the fully p&l
Marseille: Model that merges, if that's the question.
Marseille: But I still expect the divergent and then about flatness was what's the status for
Marseille: The medical study of the flatness problem. And here I can be very concise and precise. I will say that yes we're focusing on this that the 3D English we perform the first as very acts.
Marseille: As an exploratory work.
Marseille: We explored the case of
Marseille: The three damnation. The concert at your mother just to understand what we need for then we are they be performed. But he still unpublished and to be polished the
Marseille: Computation in the for the that the three k's in fourth dimension STD STD, and we add the code ready to run for the delta three and in the epl for the API model.
Marseille: However,
Marseille: There's a little bit more work still needs to be done and
Marseille: Some German German geometrical inputs. For example, we, we still need to define the
Marseille: Boundary data precisely
Marseille: And just to add that one last problem. So the complication with the new metrics is not really in the number of vertices, but his modem, the number of internal feces.
Marseille: And yes, apart from the metrics or the cases we looked at for women are just
Marseille: Bonded internal feces so that
Penn State: Thank you very much. So in this case, for example, for the delta three calculation. I just want to understand the viewpoint.
Penn State: Supposing this one calculation showed that it is, in fact, that then would you would the point of view would be a while. But yes, but that is too simple, and we should look at more complicated configurations
Penn State: And conversely, if we found that in this configuration. It is not flat would one then say that, well, if it's not flat already so therefore it will not be a flat elsewhere. What kind of is a viewpoint about
Marseille: So, here there are two questions.
Marseille: Curve geometries allowed them second
Marseille: Semi classical of
Marseille: The model the right one. So, for the third first question, I think. Yes, that that the three and not the analysis of the parallel to the in the free
Marseille: Triangulation will be announcer for the second question.
Marseille: I would say no, it's not an answer.
Penn State: Right. But the first question. If you are equal to zero. Would you not say that. Well, yes, it is zero, but that is because this is
Penn State: Our special configuration and therefore not. In other words, if you found that it is non zero, then it will be an answer, but if it is zero, then you will not really even answer is not your viewpoint. I'm just trying to understand the viewpoint, so
simone: Yes, yes.
simone: Yes, yes, it's a non trivial test. So if he fails it. That's kind of definitive in the negative. But if he passes eater, you can still check for more or less reveal tests. So yes, the answer your question is yes. Yeah.
Hal: This is how a bard two quick comments.
Hal: Just connecting things that there was a request from the viewpoint for PCI, and there are a couple of things I can comment on there so Carlos mentioned the the quantum defamation. The queue defamation and the, the capacity for that to to regularize the divergences
Hal: And mission and vojtech and outdoor retailer and I worked on this and we worked on in particular on a complex assignments theory approach. And in that context, you, you do seem to get this regular rate regulation of the divergence is we studied at a single vertex level.
Hal: And and it's interestingly what we find is that you have to fatten your spin networks. So you have to go to a tubular neighborhood of the spin network.
Hal: And it seems to me this connects with the recent work of Danielle aprons at the at the Levine and they're on Friday.
Hal: Where they're studying an extension of the cemeteries on spin networks to sort of conquer asymmetry, instead of just Lawrence group symmetry, where they're also finding fat and spin networks. So there's an interesting connection there between the cemetery algebra.
Hal: The charges of the theory and and this regulation of divergence is
Hal: Second comment in a totally different line.
Hal: BIANCA Dietrich and Seth, a song and I have been thinking a lot about area calculus recently area, Reggie calculus.
Hal: And in particular, we've been going in this direction that Simone Simone. A was pointing towards thinking about area angle Reggie calculus.
Hal: And the hope is to better understand the gluing even at the classical level and then to try to character I spend from models by how your
Hal: How your gluing is imposed. So if I take two for simplicity's like glue them along a tetrahedron. I could imagine trying to take a coherent state for that tetrahedron and perfectly glue them or I can relax that gluing and try to understand what's going on. So we've been very much
Hal: going in this direction. So Monday.
Hal: was mentioning of trying to understand better what all the conditions that come out of a certain model me
pullin: Okay. So are there other outstanding issues or should we start thinking about wrapping this up.
FAU: I just wanted to make our mark that I agree with with with Carlo that these issues are going to be settled when we actually do calculations of physically relevant things and
FAU: I mean there's there's some, there's some hope or expectation that the proper vertex might
FAU: Get rid of that divergence is also but that's something that hasn't been tested yet. It's something I'd like to do
FAU: Sometime soon, but there are definitely a paths forward and in different directions.
Penn State: Yeah, I think we can wrap up. It has been already
Penn State: Like later.
pullin: Okay, so let's thank the speakers.