Jorge Pullin: Before speaker to this will see a lot of ways, will speak them accomplish rejection, please go ahead.
José de Jesús Padua Argüelles: And thank you again, thanks to the organizers for inviting me to be in this talk.
José de Jesús Padua Argüelles: So yeah I will be discussing complex versions of the rejection how this relates to go select violations, and I wish your applications to consume cosmology.
José de Jesús Padua Argüelles: My talk will be based on these papers that I quoted with young quality and say the sentence, and we also collaborated with the NGO.
So.
Okay.
José de Jesús Padua Argüelles: So here's a map of the frog.
José de Jesús Padua Argüelles: First, I would like to justify why complex actions are interesting at all for quantum gravity.
José de Jesús Padua Argüelles: But I will be discussing a particular complex section, which is the complex rejection, so I will spend like the first half of the top discussing it, I would say some basics of it.
José de Jesús Padua Argüelles: And then I will show how when when conceive exhilaration rejection some particular configurations which violate some causality notion, and can also be related we having a spatial topology change make the action complex.
José de Jesús Padua Argüelles: And I will also continue what happens is.
José de Jesús Padua Argüelles: When you says complex arguments.
José de Jesús Padua Argüelles: For a complete certification of the rejection and in the second part that will apply these notions to to a quantum cosmology model, in particular the it will be there no boundary proposal.
José de Jesús Padua Argüelles: And we will be using that God loves his theory to evaluate the gravitational potential and that will finalize by discussing and giving an overview of work to come.
José de Jesús Padua Argüelles: Okay.
José de Jesús Padua Argüelles: So, why would someone be interested in having complex actions.
José de Jesús Padua Argüelles: The first reason is something practical, which is that even is to consider a lorenzen quantum gravity but integral or low and cigarette butts in progress in general, these are of dlc lottery buying types, they are highly signatory because of their face.
José de Jesús Padua Argüelles: And therefore, they require a very, very numerically demanding computations any particular Monte Carlo methods usually fail so in order to overcome these methods have been proposed.
José de Jesús Padua Argüelles: Examples are the perfect really inflow method.
José de Jesús Padua Argüelles: And lifted symbols and both of these recording a complexity of the action, the idea is that one has an original integration domain for the real time, integral and then everything is complexity fi.
José de Jesús Padua Argüelles: And one wants to the for the integration domain.
José de Jesús Padua Argüelles: into one, that is, in which, for example, multicultural methods can be applied and the installations are our team.
José de Jesús Padua Argüelles: Okay, so we will be focusing ellipses symbols and, as I said, we will be working with the rejection, but the the sort of.
José de Jesús Padua Argüelles: method has also been applied in the lower fee gradient flow set up by a year last last year.
José de Jesús Padua Argüelles: no reason to to consider this I mean actually the ellipses symbols have also been applied in steam forums.
José de Jesús Padua Argüelles: and
José de Jesús Padua Argüelles: yeah the yeah these these methylation themes, as we will see can verify some server generalization of of analytical continuation and there's also been recent work on analytical continuation of steam phones.
José de Jesús Padua Argüelles: And this kind of setup also allows us to have some something general to to consider signature mixing in the path, integral and by that I mean considering both up and and the race and contributions.
José de Jesús Padua Argüelles: and related to this idea of generalizing the integration domain of the path integral recently, it has also been proposed that the potential in quantum gravity should be defined over complex matrix this was in this paper last year.
José de Jesús Padua Argüelles: And it's also been applied in the context of the Nova under a proposal by these authors.
José de Jesús Padua Argüelles: And we will see that also this relates to having I mean, so this idea of something of a complex matrix is also.
José de Jesús Padua Argüelles: has also been discussed before in the mid 90s by Luke on salty which is either having a spatial topology change changing configurations in the bathroom and we will encounter this in the context of rejected.
José de Jesús Padua Argüelles: So let me then begin by giving some basics of what reggie calculus.
José de Jesús Padua Argüelles: And this is a notion that shows up in many lattice like approaches to quantum gravity, for example, dynamic tribulations.
José de Jesús Padua Argüelles: quantum reggie calculus and also spin forms and it seems to be not has found applications in numerical general relativity.
José de Jesús Padua Argüelles: So the general idea is that one is to win the skirt ISIS GR by truncated the degrees of freedom and the way this is only by triangulating regions of space time.
José de Jesús Padua Argüelles: And the strangulation is done by considering higher dimensional variations generalization so of triangles can simply says so, for example in 3D they are tetrahedron and for the I will be referring to them as for synthesis and this is an example of what a triangulation those.
José de Jesús Padua Argüelles: Something like this, so we are replacing a continued manual by.
José de Jesús Padua Argüelles: The piece was flat viewing of geometries and in this way, the metric information will be included in the segments this lens.
José de Jesús Padua Argüelles: and
José de Jesús Padua Argüelles: A way to do quantum reality, these ways to associate that transition amplitude to a triangulation by fixing the geometry of the boundary and then integrating over the geometry of the book, which is what I want everything here.
Abhay Vasant Ashtekar: Is the geometry and the boundary always going to be real for you.
Abhay Vasant Ashtekar: Because you gave us some motivation, why complexes and, in that you know to tame the pathological but yeah the physical question is really calculating amplitude from 111 physical state to another physical state so.
Abhay Vasant Ashtekar: Talk to talk out of the boundary States going to be referring to the real lauren's in geometry.
José de Jesús Padua Argüelles: Yes, yeah they would be okay.
José de Jesús Padua Argüelles: Well, no, actually.
José de Jesús Padua Argüelles: yeah yeah they would be.
Abhay Vasant Ashtekar: Okay, thank you.
Abhay Vasant Ashtekar: Okay.
José de Jesús Padua Argüelles: yeah thanks for the question.
José de Jesús Padua Argüelles: So yeah when one considers something like this, this I think ago.
José de Jesús Padua Argüelles: And the exponent can be an adaptive version of see the items, the last thing he would action or it can also be minus the Euclidean action okay.
José de Jesús Padua Argüelles: So one needs to find their family vacation of the of the Einstein he would actually to be discreet is geometries, and that is called the rejection.
José de Jesús Padua Argüelles: And the basic idea of it is that there's a notion of curvature that can be identified in.
José de Jesús Padua Argüelles: In so simply says, have a triangulation of dimension to that I will referring to as bones, so the basic idea is shown in these two dimensional example now the bones are just points, and we have arguing of triangles.
José de Jesús Padua Argüelles: And what can consider all of the the hero angles in the triangles that mirror that vertex and also the angle circle, I said that vertex and go through the sum of all of these angles.
José de Jesús Padua Argüelles: If this configuration can be embedded into flat space without breaking these glowing.
José de Jesús Padua Argüelles: Then, this will be flat and actually this corresponds to all of these angles, something to play in up in geometry.
José de Jesús Padua Argüelles: If they fail to some to buy, then we have a deficit angle, which will be the difference between these two pi and there's some of these angles and that these will give us the notion of curvature.
José de Jesús Padua Argüelles: So here so, for example, this flattened version in 3D now the curvature will be localized that segments, I mean for the curvature will be localized at triangles.
José de Jesús Padua Argüelles: So the idea of the reaction is to observe that the isolated action is some notion of curvature localizing appoint weighted by a volume element associated to work this.
José de Jesús Padua Argüelles: quarter is localized.
José de Jesús Padua Argüelles: And in the in the rejection, we have curvature associated two triangles and we will wait them by the area of the triangle, one can also add cosmological constant term and we we do so.
José de Jesús Padua Argüelles: By now considering the volume of of the first thing PCs.
José de Jesús Padua Argüelles: Oh hey I should know is that.
José de Jesús Padua Argüelles: No de niro to compute this deficit angles, the discussion can always be.
José de Jesús Padua Argüelles: Taking to just do the because what if we starting to the then I mean we're already into the then if we have any 3D we can collapse, the bone.
José de Jesús Padua Argüelles: orthogonal II, by doing a prediction, in order to obtain something that seemed to me and in 3D we can do this in 4d we can do the same, by doing an orthogonal projection of the triangle this this angle, we want to consider.
José de Jesús Padua Argüelles: So, in particular, if the triangle is space like, then we will be considering I mean cubs game, and if the triangle, in his timeline, then we will be considering a Euclidean angle, so let us recall how this angle started define because he's.
José de Jesús Padua Argüelles: A certain theorizing.
José de Jesús Padua Argüelles: So up that I was can be defined easily we just have.
José de Jesús Padua Argüelles: If I can see two vectors I can consider the redefined by these two vectors and see where it intersects the unit Chico.
José de Jesús Padua Argüelles: The weights defined by these to raise will give me an Arc in the unit circle, and then the angled we just be the nuclear length of set up.
José de Jesús Padua Argüelles: We would like to use, I mean if one tries to generalize this to the mikulski angle, we know that the unit simple is that are actually two high paperless.
José de Jesús Padua Argüelles: And therefore, one can only use this notion when the to race.
José de Jesús Padua Argüelles: can be yeah they intersect the same hyperbole branch, as shown here, so we can define that angle by just consuming again the link, but now lorenson length of this Arc and this gives us the usual articles formula here.
José de Jesús Padua Argüelles: Which is some sort of analytical continuation of the same formula and Euclidean geometry.
José de Jesús Padua Argüelles: But then the question arises Okay, what happens if I have a which that connects the first quadrant and the sequence.
José de Jesús Padua Argüelles: Or the first and the third, etc.
José de Jesús Padua Argüelles: intercepted We only need to define these angles between for a wedge in the first quarter and angles, for which, in the first and second quadrant.
José de Jesús Padua Argüelles: and the rest of the angles, can be defined by just imposing relativity and the way the street, the angle between the first and the second quarter easy fine.
José de Jesús Padua Argüelles: he's very performing an analytical continuation.
José de Jesús Padua Argüelles: First, I consider that I have two vectors in the first quadrant.
José de Jesús Padua Argüelles: And then I will take one of the vectors to cross the light gone.
José de Jesús Padua Argüelles: And then become tangling.
José de Jesús Padua Argüelles: When doing so, if I take a look at this formula for example i'm dividing by the norm, of the vector so that's us the square of the norm Square and if it becomes time like, then this will give me an imaginary part.
José de Jesús Padua Argüelles: And they're here the important part is that there's an ambiguity to what I consider to be the square root of minus one, it can be I or it can be mindset.
José de Jesús Padua Argüelles: And the final result is that for each time I, which causes a light come.
José de Jesús Padua Argüelles: The angle, will become an imaginary part of plus or minus it over to.
José de Jesús Padua Argüelles: And therefore lawrenson Anglesey in principle can be complex.
José de Jesús Padua Argüelles: be finding this way, then it gives the plane spans.
José de Jesús Padua Argüelles: A total angle of plus or minus to buy and again this plus or minus comes from the mbu to crossing delightful.
José de Jesús Padua Argüelles: OK.
José de Jesús Padua Argüelles: So, now that we know what the flat value of of them includes complaint is, we can define a deficit angle by discussing the difference, you know analogous to what I explained before.
José de Jesús Padua Argüelles: And here, an important point that rises, which is that it could be.
José de Jesús Padua Argüelles: That there's some of these angles cannot cancel this imaginary part in the for the flat value, and therefore the deficit angle.
José de Jesús Padua Argüelles: can have an imaginary part and when put in the action, these can produce a real fight for the exponent so that we can have configurations that are exponentially enhance and exponentially suppressed.
José de Jesús Padua Argüelles: We will call this sort of configurations.
José de Jesús Padua Argüelles: gasoline irregular or say that they have any way we like as a structure or, more precisely, we should say that they have any regular life structure, and this is a sort of evaluation that we call Kinshasa evaluation.
José de Jesús Padua Argüelles: Still.
José de Jesús Padua Argüelles: This king's Castle violations can be.
José de Jesús Padua Argüelles: studied as follows, so it's a situation that i'm showing here, you know.
José de Jesús Padua Argüelles: suppose that I have a bone and three triangles meaning at that bone.
José de Jesús Padua Argüelles: It could be that when I can see all of the triangles in order to go around the bone i'm.
José de Jesús Padua Argüelles: yeah yeah I can curse any number in principle of lights of of light rays.
José de Jesús Padua Argüelles: So, and in any capacity space or or in general flat tribulations then when I go around the bone I will.
José de Jesús Padua Argüelles: Have for light comparisons, in total, which is what happens in in the COPs the space, for example, so in that way, I will always cancel this.
José de Jesús Padua Argüelles: imaginary part that comes in the backseat and, but I could also have something that like this configuration, in which I am doing eight like comparisons.
José de Jesús Padua Argüelles: And these will therefore we're not cancel the imaginary part Okay, so this is just a regular in the sense that we have a bone that has more or less than two like guns were, for example in in in makovsky spaced which phone point we have yeah in each point we have exactly two like.
Okay.
José de Jesús Padua Argüelles: So he does other this kind of gasol your regular configurations can be linked with spatial topology change.
José de Jesús Padua Argüelles: And I would like to illustrate these, but before, let me remind you, a bit of triangle inequalities in costly space, because they.
Abhay Vasant Ashtekar: are referring to the nation spaces.
Abhay Vasant Ashtekar: Are the.
José de Jesús Padua Argüelles: auto yeah I mean.
José de Jesús Padua Argüelles: yeah the examples that i'm discussing will be so the conceptual example for this topology change will be two dimensional, but this is causality validation can happen in any dimension.
José de Jesús Padua Argüelles: And it's just that.
José de Jesús Padua Argüelles: yeah I have an imaginary, that is, Daniel coming from the fact that when I do this projection to to be by collapsing, the bone.
José de Jesús Padua Argüelles: Then I will see that the deficit angle or there's some of these angles covers more or less than two line items.
Abhay Vasant Ashtekar: But what it has to be topology is not obvious if we're just doing projections right because we're putting the topology and four dimensions and then it's not.
Abhay Vasant Ashtekar: clear to me that.
Abhay Vasant Ashtekar: It is telling us anything about topology change or anything in 40 minutes.
José de Jesús Padua Argüelles: yeah yeah you're right in fact in.
José de Jesús Padua Argüelles: The animation higher than for.
José de Jesús Padua Argüelles: These two ideas.
José de Jesús Padua Argüelles: So so it's not true that.
José de Jesús Padua Argüelles: In that each time you have a king's college population, you have a space or spatial topology change.
José de Jesús Padua Argüelles: But I will think that the other way it works.
José de Jesús Padua Argüelles: Is that answer your question, so there are nothing one to one correspondence with they are related.
Abhay Vasant Ashtekar: But you're saying in 40 mentioned the other one to one correspondence.
José de Jesús Padua Argüelles: know they are.
Now.
José de Jesús Padua Argüelles: yeah and actually the example that we're consuming cosmology is not official policy change well.
Laurent Freidel: So yeah.
Laurent Freidel: into the into the they are right.
Laurent Freidel: In to meet me because of religion too big change.
José de Jesús Padua Argüelles: yeah I don't know approved but intuitively I would say that that it's true.
José de Jesús Padua Argüelles: That that into the there in one to one correspondence with the example that we have in in 4d, although it is a special w change because we are considering like universe popping out of nowhere.
Laurent Freidel: yeah I mean I would imagine if you have a code violation, you need to have a temperature change because if you had smooth apology, you would ever you know causal evolution for it.
Laurent Freidel: You have a slight if you have a local slicing of your space time, then you have to like cohen's you.
know.
Bianca Dittrich: To clarify just to suppose I didn't know not to get hung up on that point in this case of democratization, the different kinds of causality violations.
Bianca Dittrich: And causality rules which are we actually have been introduced by not annoying for cvt and it's not very clear vision for instance hinge causality.
Bianca Dittrich: What is the relation between hinge causality and say a similar environment for higher dimensional bidding books.
Bianca Dittrich: So in 2d it seems to assess a one to one correspondence and higher dimensions, we believe that tells us lead always to hinge causality violations and complex actions, but there is no proof yet.
yeah.
Bianca Dittrich: So maybe yeah so we have a short discussion with the people if you're interested but it's something which is not which doesn't seem to be the next year.
José de Jesús Padua Argüelles: Okay, so interview, let me show how this can be linked to the velocity change.
José de Jesús Padua Argüelles: But before that, yes, I was saying, let me say a few words about the triangle inequalities.
José de Jesús Padua Argüelles: And let me go see.
José de Jesús Padua Argüelles: A triangle that only has space like ages, as shown here.
José de Jesús Padua Argüelles: And, for example, if I take a look at this HQ.
José de Jesús Padua Argüelles: I can see that it can be boosted into into this segment in the horizontal line, and therefore the length is just simply the length of the segment and likewise for this edge, I can see that the edge of this, the length of these edge is simply the length of the segment.
José de Jesús Padua Argüelles: And therefore I see that there's some of the length of these two edges it's actually less than the length of this opposite edge and therefore the triangle new qualities is inverted.
José de Jesús Padua Argüelles: And, in particular, we can also notice that, in the vertex opposed to this greater edge.
José de Jesús Padua Argüelles: We have a light on, because this is.
José de Jesús Padua Argüelles: A white which.
José de Jesús Padua Argüelles: is like the first and third quadrant.
José de Jesús Padua Argüelles: So in this case you're trying any qualities and inverted in the led the vertex opposite to the to the greater edge, I have a light.
José de Jesús Padua Argüelles: And I can also consider these type of triangle, in which I have to space like edges here in with and one time, like edge in blue.
José de Jesús Padua Argüelles: These type of time it's completely unconstrained I have no light Cone in this vertical, but I must have a lightweight in these vertices here because i'm connecting the first and the second okay.
José de Jesús Padua Argüelles: So in the upper limit you considered this type of triangulation of four triangles meeting and appoint.
José de Jesús Padua Argüelles: And I because you were the first case in which everything is space like an ar and b are, the greater edges, so that, obviously, to them, I always have a light on and there we immediately see that.
José de Jesús Padua Argüelles: I have for lichens meeting at these these tactics, so these would be a castle irregular configuration and if I it will, therefore, we not flat because i'm not canceling the N minus plus or minus two by I.
José de Jesús Padua Argüelles: Am if I am babies in 3D and we have some sort of trouser.
José de Jesús Padua Argüelles: Space thing.
José de Jesús Padua Argüelles: I can see the two like guns as going from the left or from the right leg and then other to as going from the from the I guess front and back of these these two here.
José de Jesús Padua Argüelles: And then, for the other case in which I have less than two labels, I can consider the situation in which again A and B airspace like.
José de Jesús Padua Argüelles: and see stang like so because they have time like time like and then space like.
José de Jesús Padua Argüelles: I, we have no like increasing in this which and therefore, in total, I have no life and crossing from the small.
Simone SPEZIALE: example Sir one plus one or two plus one or.
José de Jesús Padua Argüelles: This one.
José de Jesús Padua Argüelles: yeah plus one.
Simone SPEZIALE: One plus one so time is vertical and spaces, or is it.
José de Jesús Padua Argüelles: yeah yeah.
Simone SPEZIALE: So I don't understand, can you go back to the first one, then I got confused.
Simone SPEZIALE: So besides time like direction here right.
José de Jesús Padua Argüelles: Now, oh no no Okay, so that the documents in the left our time is going up, but the dang thing they were in the right I just skim article.
José de Jesús Padua Argüelles: yeah I mean yeah they cannot be embedded into into something to do because they are not.
Simone SPEZIALE: So so you're not doing one plus one were you doing.
José de Jesús Padua Argüelles: yeah I mean i'm doing one of those whining the sense that that would be like the signature of the building blocks the triangles.
José de Jesús Padua Argüelles: But yeah I mean this is not me cause space.
Simone SPEZIALE: Well suppose he was I don't understand what the case in which the deputy dangle is zero.
Simone SPEZIALE: When we look like just understand your picture I don't understand the meaning of your picture isn't there, yes.
José de Jesús Padua Argüelles: yeah so so the case in which, in which I tried everything possible to embed this kind of configuration into bankruptcy space.
Simone SPEZIALE: Okay, what is this kind of configuration will be, can you characterize it then.
José de Jesús Padua Argüelles: yeah or legislative space, like a space like and i'm also considering the position in which.
José de Jesús Padua Argüelles: A and B are greater than to see.
José de Jesús Padua Argüelles: Okay, so see is the is the length of these diagonals here.
José de Jesús Padua Argüelles: That complete these four frames.
Simone SPEZIALE: So.
Simone SPEZIALE: Usually, what I tried to do is okay, first of all, if they're all ages or space like these triangles are all for four triangles you want right that's what you said yes yeah.
Simone SPEZIALE: So they will all be rather squashed and now you want to know whether they can share you want them to share one of the vertices and then compute the devotee dangles at the vertex.
Simone SPEZIALE: If that's what you usually do right.
José de Jesús Padua Argüelles: yeah.
Simone SPEZIALE: So you will never look like what you're doing here in which be is obviously time like.
Simone SPEZIALE: Really, the question but.
Simone SPEZIALE: Because i'm confused.
José de Jesús Padua Argüelles: I don't know.
Simone SPEZIALE: The logic of your presentation.
José de Jesús Padua Argüelles: Okay yeah I mean, so this is just.
José de Jesús Padua Argüelles: yeah it's a cartoon Okay, this is not to think of as embedded in makovsky space, I just have so what this cartoon is telling me is, I have four triangles meeting at a point.
José de Jesús Padua Argüelles: And then I have extra information that will make this not embeddable into the space that say a and we have to be space, like in the sense that their length squared is positive.
Simone SPEZIALE: Okay.
José de Jesús Padua Argüelles: and see so so I mean, yes, the square, this will also be positive and then, if I take the square root of those numbers, I have to take the same position to account.
Okay.
José de Jesús Padua Argüelles: And then.
José de Jesús Padua Argüelles: let's take or did.
Laurent Freidel: I, if I can add I think what he's saying is that.
Laurent Freidel: Would you also say.
Laurent Freidel: Is if I go for these triangle, each one of these strangled we carry you're like Oh, and so therefore I will have for like on.
Laurent Freidel: It and I because of singularity.
Laurent Freidel: Now it's not embedded bullies in 2d but it's unbelievable in 3D and that's the right hand side.
Laurent Freidel: And then on the right hand side deals and rhonda for like coins, but they should be to like going on the you know one like to like I mean one past like on the Left leg and allopathic on the Left leg and then is to like Cola.
Bianca Dittrich: Yes, yeah and he will be useful to see depending on.
Simone SPEZIALE: The case in which you can embed them with a unique well defined like on.
Bianca Dittrich: ya know but, but this this you can easily fall, but first of all, you can see the light cones if you look very carefully on the total.
Bianca Dittrich: And we can Mona the picture, with a towel, together with one tying it.
Bianca Dittrich: makes us happier, so the vhs I actually have athletes.
Bianca Dittrich: go around the next, for instance.
Bianca Dittrich: So.
Bianca Dittrich: nothing to do with time, but, of course, if you want to imagine a regular triangulation just single to be on time we make, and then just making a case.
Bianca Dittrich: that's not what we know what his own.
José de Jesús Padua Argüelles: yeah let me show you, so this is an example of something you may want to be, you can think of this as just becomes the space and then you blue four triangles around the origin.
Simone SPEZIALE: yeah but no they're not space, like the edges of these triangles right.
José de Jesús Padua Argüelles: yeah I.
Simone SPEZIALE: don't know if I was following, then you kind of lost me when you change the logic of the representation in this next picture.
José de Jesús Padua Argüelles: yeah okay.
Simone SPEZIALE: anyway.
José de Jesús Padua Argüelles: The explanations yeah No, let me actually yeah I can I can I have this picture that we actually recommended.
Bianca Dittrich: This point is that there is no very defined flow of time, so it's a bit difficult to.
Bianca Dittrich: put all.
Bianca Dittrich: The time connection kind of push.
Simone SPEZIALE: But I guess, this is what do you wanted to explain so starting locally.
Simone SPEZIALE: You know.
Simone SPEZIALE: One triangle, we have a causal structure.
Simone SPEZIALE: But then there might be obstructions when you glue them together.
Bianca Dittrich: The Mona in the interest of time we can do all we can provide you with a picture on whether you should maybe.
Simone SPEZIALE: No, no, no, please don't sorry.
José de Jesús Padua Argüelles: No, no it's okay it's.
Simone SPEZIALE: funny you.
Simone SPEZIALE: know just go ahead, thank you.
José de Jesús Padua Argüelles: Okay well yeah we can yeah we can discuss it later.
José de Jesús Padua Argüelles: So yeah in this case it's it's.
José de Jesús Padua Argüelles: yeah we do the embedding into 3D we you can see sort of gap and it's also called a journal.
José de Jesús Padua Argüelles: So, then the question yeah another interesting question is whether this kind of spatially.
José de Jesús Padua Argüelles: topology changing processes should contributed to the path integral.
José de Jesús Padua Argüelles: And there are arguments, both for and against that, so I go in store, is that.
José de Jesús Padua Argüelles: it's been argue that this so called frozen topology framework live to live to inconsistencies like spin statistics regulations.
José de Jesús Padua Argüelles: But then there's there are some arguments against these which point out that is one considers to scale our field propagating in a trouser then there's like an infinite burst of energy in the crutch.
José de Jesús Padua Argüelles: And therefore yeah The conclusion is everyone should actually exclude this type of this type of geometry.
José de Jesús Padua Argüelles: And then the work of Luca and certain that I put it before.
José de Jesús Padua Argüelles: kind of.
José de Jesús Padua Argüelles: implies or I use that once you to press the stressor like configurations, so that they they cancel the singularity coming from from the matter fields propagation.
José de Jesús Padua Argüelles: And if we go back to the complex.
José de Jesús Padua Argüelles: Sorry, to their reaction.
José de Jesús Padua Argüelles: The suppression can be achieved in if we choose the proper sign for the plus or minus I I buy over to so that when you have more than two lightness around the bone, then you have a negative imaginary part in the index.
José de Jesús Padua Argüelles: But this would ultimately make the john mood like configurations to be exponentially enhance.
José de Jesús Padua Argüelles: and
José de Jesús Padua Argüelles: yeah we bianca says, and I tried before in the context of effect extreme forms to consider these these prescription and we noticed that when computing expectation values using this exponentially enhanced configurations they basically ruin the expectation violence.
José de Jesús Padua Argüelles: So concluded that maybe they should not be added and actually approaches like cdt exclusively for with this kind of huge causality violations.
José de Jesús Padua Argüelles: Here i'm using a little language i'm saying prosser like and and JEREMY like but as we discussed in higher dimensions, this could be.
José de Jesús Padua Argüelles: Something that's not related with topology change so dress the like only means that I have more than two lifetimes and German like means that I have listened to, like okay.
José de Jesús Padua Argüelles: So that was.
José de Jesús Padua Argüelles: A way in which the rejection can become complex by just consuming lawrenson geometries but what one could also consider.
José de Jesús Padua Argüelles: Complex arguments or the rejection, as I mentioned, and the rationale for these can be just do the computation is using these websites single method or just to sum over complex geometry So this has been proposed, recently, and for that we will need to define a notion of complex angles.
José de Jesús Padua Argüelles: which can be found through a complex matrix so one way to do so is to not consider two vectors into the but that live in situ.
José de Jesús Padua Argüelles: and define an inner product view and by the start here, and that is used by linear form Okay, so this in particular gives me.
José de Jesús Padua Argüelles: I mean it satisfies that when I can see everything to be real, this is just the up the matrix and if the first entry is purely imaginary and the second real, then I have them in documentary so the general ISIS both cases.
José de Jesús Padua Argüelles: But this turns out to be.
José de Jesús Padua Argüelles: To general for our purposes, and we can see.
José de Jesús Padua Argüelles: My version of us, which is a generalized week rotation in which the vectors are taking to be in our two.
José de Jesús Padua Argüelles: And because you're the star pro that can again recovery plan and mikulski geometries and you have these big rotation angle five.
José de Jesús Padua Argüelles: In this way we can find two versions of the.
José de Jesús Padua Argüelles: Of the angles.
José de Jesús Padua Argüelles: Being by this data.
José de Jesús Padua Argüelles: And they were shows differ by how I take the branches of discourse and of the lower barriers so here the notation is that if it's close then i'm taking the analytically continuing from the Opera happening, and if it's nine years, then i'm doing so from the lower half thing okay.
Abhay Vasant Ashtekar: So.
Abhay Vasant Ashtekar: Each value to you no problem.
Abhay Vasant Ashtekar: So, so you got one parent or family or start products.
Abhay Vasant Ashtekar: Not in the product and angles.
José de Jesús Padua Argüelles: Exactly yes.
José de Jesús Padua Argüelles: Okay, and then you particularly will reproduce Euclidean angles and lorenson angles up to science and factors of I that I would I will discuss this in an interview.
Okay.
José de Jesús Padua Argüelles: And just for completeness me say that, starting from this one can we express this to our product in terms of complex links squared of the triangle defined by two vectors.
José de Jesús Padua Argüelles: resulting in this type of formula that we will not use, but I should mention this ad is the square.
José de Jesús Padua Argüelles: area.
José de Jesús Padua Argüelles: And one can then complexity by the this link squared undefined.
José de Jesús Padua Argüelles: Complex angles, these way, and this was done by the other thing that I mentioned before, in the context of the old morphic very slow Okay, but we will be focusing this type of thing.
José de Jesús Padua Argüelles: You see, like.
José de Jesús Padua Argüelles: So therefore we have to wear shoes hit the plus and the minus for these these complex angles, that will allow us to find a complex efficient angle.
José de Jesús Padua Argüelles: And they differ by your choice of branches for the logarithms and squirrels and they satisfy the following properties, if I take five.
José de Jesús Padua Argüelles: To lie in zero to two pi then feet up last reproduces manresa up an angle as fi approaches you from above, and it reproduces minus I times the the same angle, if I approached by from below, but these loans and angle already has a specific assignment for crossing the.
José de Jesús Padua Argüelles: The library any particular these will be the negative particulars Okay, and similarly.
José de Jesús Padua Argüelles: I have yeah I have similar results.
José de Jesús Padua Argüelles: For Peter minds.
José de Jesús Padua Argüelles: And then the idea is that we can analytically extend both either plus and the minus two periodic functioning functioning fine and they have period of four by okay and that's the kind of complex angles, that we will consider I can then use them to find.
José de Jesús Padua Argüelles: A complex exponent.
José de Jesús Padua Argüelles: So we have here yeah these complex responding to be a complex question of the.
José de Jesús Padua Argüelles: Of the reggie explain that I mentioned before the visit angle, we now have will be this either summer difference of two pi which will be the flat value of the complex angles, and then we have the.
José de Jesús Padua Argüelles: The the hero angles.
José de Jesús Padua Argüelles: Already, though, after after doing this prediction and then this notion of gravity will be waiting by the square root of the area Square.
José de Jesús Padua Argüelles: And then we have a cosmological constant there and again, we see that we have a specific.
José de Jesús Padua Argüelles: prescription for the branches that we choose and for the sense that we choose, and these are chosen, so that the following is satisfied for gasoline regular configurations, the two experience will be the same.
José de Jesús Padua Argüelles: And, depending on the value of five I would reproduce either.
José de Jesús Padua Argüelles: Items generation X.
José de Jesús Padua Argüelles: minus minus eight X generation action and plus or minus the up then action Okay, so we see that we are covering lawrenson geometries with plus and minus is in the explain and also Euclidean geometries with plus and minus signs in the explain.
José de Jesús Padua Argüelles: And I should point out, for a regular like the structures we this experience will not be the same, and the actions also will not be the same, and this comes, because now.
José de Jesús Padua Argüelles: yeah, we will not be able to consider these two by here and that's just because and.
José de Jesús Padua Argüelles: That makes the ambiguity in defining the learning Center angles relevant for discuss any irregular relations.
José de Jesús Padua Argüelles: Okay, so, in summary, for this complex reggie calculus.
José de Jesús Padua Argüelles: The lawrenson reggie Jackson has an ambiguity associated to wedges containing light rays.
José de Jesús Padua Argüelles: When we complexity Phi this ambiguity.
José de Jesús Padua Argüelles: So sorry when we completed by the ambiguity is associated with the branch guts of the complexity fight action.
José de Jesús Padua Argüelles: And that's reasonable because an ambiguity, we mean that these configurations will be multi value, and therefore we, I mean that's that's the notion of that's where the notion of banquets trench coats comes in.
José de Jesús Padua Argüelles: The end up going into this and imaginary back to the action when we have an irregular legend structure.
José de Jesús Padua Argüelles: And these will give us exponential enhancements or substations in the bathroom.
José de Jesús Padua Argüelles: And then, this irregular electron structures can be associated with special couple any change.
José de Jesús Padua Argüelles: can be okay.
José de Jesús Padua Argüelles: And the yeah the interesting question is whether these irregular configurations or whether topology changing processes should contribute in the passing through.
José de Jesús Padua Argüelles: So that's about for complex rejection and I now I would like to apply these notions to to cosmology so it would be a nice place to ask for questions in this first part training.
José de Jesús Padua Argüelles: If not, then let me, let me.
José de Jesús Padua Argüelles: Go to the second part.
José de Jesús Padua Argüelles: So we will be considering the no boundary proposal and, let me first say a few words on what he sees in the India continue so, because here, this is our is our w metric for a close universe.
José de Jesús Padua Argüelles: And the idea is that we will be doing mini super space, but in the world computations that will give us transitional pages from going.
José de Jesús Padua Argüelles: From an initial scale factor to our finance scale factor.
José de Jesús Padua Argüelles: And it all started when it goes to this mini super space that's integral I can do the.
José de Jesús Padua Argüelles: The potentially a explicitly so that the finance versus transition it to look like a final dimensional integral.
José de Jesús Padua Argüelles: That I showed you.
José de Jesús Padua Argüelles: Where these calligraphic n.
José de Jesús Padua Argüelles: is basically the.
José de Jesús Padua Argüelles: The laps risky like a but also gets fixed to be constant.
José de Jesús Padua Argüelles: So yeah I wouldn't be referring it as as the laps but I that's being a little sloppy and this effective action.
José de Jesús Padua Argüelles: is written here, so we see there, it depends on the cosmological constant on these labs on the initial and final values from scale factor, and also the on the curvature of the station slice which we said to be one.
Abhay Vasant Ashtekar: so important for you the topology is closed, is a straight not not allow the open to politics.
José de Jesús Padua Argüelles: yeah yeah it will be important as yeah as I will discuss now.
José de Jesús Padua Argüelles: And I don't think the regulation, we can see.
José de Jesús Padua Argüelles: So this effective action that I have here.
José de Jesús Padua Argüelles: has four stationary points that can be real it purely imaginary imaginary or complex, depending on how a CEO and a one compared with.
José de Jesús Padua Argüelles: This with an effective scale factor value that is within you.
José de Jesús Padua Argüelles: So when I consider a configuration that.
José de Jesús Padua Argüelles: That gives me just a relapse, then I mean they lose your setup and then the transition empty do will mean that i'm going from a lucien.
José de Jesús Padua Argüelles: configuration to another one same configuration when it's purely imaginary then i'm going from my Euclidean where you cleaning configuration and I can also have a mixture, in which I go from Euclidean to laurentian.
José de Jesús Padua Argüelles: So the idea is something that looks like this in which I blew a chemistry of the Euclidean sphere and a hemisphere, of the lower incidence view.
José de Jesús Padua Argüelles: And therefore considered like a you clean it up and transition will be touching a transition in this first region, then algorithm to the ratio is one in the second region and the next one is linking these two hemispheres.
Abhay Vasant Ashtekar: So, but all this is really what we're talking and as a separate Gibbons and son had proposed long time ago right, so if there is a difference between what they propose or what you're going to do, could you please pain point for us because there's always a confusing thing for me.
José de Jesús Padua Argüelles: Of course yeah.
Abhay Vasant Ashtekar: So, because you don't refer to them at all anywhere, so therefore I just want to make sure that you are still following that path, and we are not yes.
Abhay Vasant Ashtekar: yeah there's no departure from me at all so far.
José de Jesús Padua Argüelles: yeah no.
José de Jesús Padua Argüelles: Sorry, we will differ from them, but in a way that is new.
José de Jesús Padua Argüelles: That is this.
José de Jesús Padua Argüelles: yeah I wouldn't go back to.
Abhay Vasant Ashtekar: You.
José de Jesús Padua Argüelles: Okay, so now you're staying with the setup.
José de Jesús Padua Argüelles: will go see.
José de Jesús Padua Argüelles: That this continuing picture can be sort of divided into into shelves, so they will be like the assurance that i'm illustrating here, so they will be portions of the nucleus few or portions of the low instance here and we would like to glue.
José de Jesús Padua Argüelles: This potions in order to serve, we believe this whole idea Okay, so I wonder if it needs to be purchase as shelf, which can be living in the Lawrence in part or in the up to par.
José de Jesús Padua Argüelles: So these are this, this is, these are the shelf that will display that's okay.
Laurent Freidel: Because they have a question that we realize the one of our Bible was so what you mentioned earlier, is that in the prescription by Jorma Lupo and soaking this would be exponentially enhanced.
Laurent Freidel: It so so in your case which, which is what working I think was having right, whereas need to rob said these configuration should be exponentially suppressed that's the big difference.
Laurent Freidel: So, in your case.
Laurent Freidel: What I mean, are you choosing yeah what choice, do you make, or is it more solid or what's the result there.
José de Jesús Padua Argüelles: yeah it's.
Laurent Freidel: it's a breast ordinance.
José de Jesús Padua Argüelles: yeah it's going to be suppressed.
José de Jesús Padua Argüelles: yeah so yeah for the hinge violations, it will be suppressed, and we are actually reproducing like the result of took okay for for the.
Laurent Freidel: For the that's why it's not it's not looking at.
José de Jesús Padua Argüelles: Exactly yeah yeah.
Laurent Freidel: But then Okay, was it so in some sense, you can have disagreeing with zuko then we're soaking somehow.
Bianca Dittrich: Just like yeah.
Laurent Freidel: You were.
Bianca Dittrich: Or is it will come later, but also to clarify.
Bianca Dittrich: Luke was talking to to sing in 2d So what we disagree with this, this is a slightly different issue, then this debate between hawking.
Bianca Dittrich: hawking and and.
Bianca Dittrich: The Lincoln choice is.
Bianca Dittrich: So here for so acadian part we find suppression and then generally for kinds of topology change and, of course, irregularities, we will also find suppression and that's where we disagree this this.
Bianca Dittrich: new coin talking, which are used a different element which was not based on geometry, but on the Meta Meta hits.
Bianca Dittrich: But welcome, so the difference, the main point here is that it is creating this reaching which, which always will be.
Bianca Dittrich: irregular which you don't have to continue so that's kind of some.
Bianca Dittrich: Additional point in which you have to decide to include or not.
Laurent Freidel: Is the idea that that the digitization somehow provides a.
José de Jesús Padua Argüelles: Clean resolutions.
Laurent Freidel: or this debate or or or this dmv to.
Laurent Freidel: have some choice.
Bianca Dittrich: know me as a debate we find also that that it's it's suppressed so that's an accordance with this.
Bianca Dittrich: offense using because if shirts.
Laurent Freidel: mm hmm.
Bianca Dittrich: You could say it's actually there's.
Bianca Dittrich: there's indication that indeed informs confirm that, because for a cleaning configuration information obviously always finds a suppression.
Laurent Freidel: mm hmm.
Bianca Dittrich: But we bring it a point somewhat further and seeing them more even more regularly to.
Bianca Dittrich: where even the action is complex, because today is actually the action it's a full events in signature it's not complex, but you have an accordion.
Bianca Dittrich: set a point you have to set appointments or cleaning so there's kind of different issues, but before we kind of find if the action itself is complex, also there we tend to prefer suppressing choice or this mm hmm.
Bianca Dittrich: So, but this kind of.
Bianca Dittrich: When it comes over in the last phase something.
Bianca Dittrich: Maybe, let me see going.
José de Jesús Padua Argüelles: yeah I will mention this, and if he's not here, we can go more into detail.
José de Jesús Padua Argüelles: um.
José de Jesús Padua Argüelles: yeah so yeah let me I was agreeing with Regulation Okay, so we have these these shells that are basically ended for the picture will be connecting to a series, so what we will do is well actually I mean what other people did before, and we are using that regulation.
José de Jesús Padua Argüelles: is to triangulate the three skew and then connect these two triangles and so if we stick together and the regulation of the three sphere we consider is the boundary of a complex Bulletin.
José de Jesús Padua Argüelles: that's called a sixth on itself, and they need to sign up, we were important for the discussion.
José de Jesús Padua Argüelles: But the idea is, we have a four year four dimensional I can't explain it has a boundary, which is also a triangulation so it's made of tetrahedron and then we blew this.
José de Jesús Padua Argüelles: To s3 together.
José de Jesús Padua Argüelles: By gluing tetrahedral together, as shown in this picture.
José de Jesús Padua Argüelles: That I took from this paper, by the way.
José de Jesús Padua Argüelles: So the building block will be this kind of.
José de Jesús Padua Argüelles: truncated dragging tetrahedral pyramid which surgical precision.
José de Jesús Padua Argüelles: And the casing which yeah so then we impose some cosmological conditions or a start up by making all of the edges in inside the initial.
José de Jesús Padua Argüelles: tetrahedron to be the same, and also for the finances are into the same so that H length we've captured the essence of the initial pilot scale factor, and then the height of this first one will be I think fight with the laps and that will be our information valuable.
José de Jesús Padua Argüelles: And then yeah I should say that this is going to be divided into interesting pieces.
Okay.
José de Jesús Padua Argüelles: So, as I mentioned the integration valuable we know we the law, the laps or the height of the system.
José de Jesús Padua Argüelles: And this will be, because this terrorism into this will be Highness lottery, so we need to.
José de Jesús Padua Argüelles: Find methods to evaluate this kind of hi Lucy letter integrals and we use the method used by took phil Berger and lemons.
José de Jesús Padua Argüelles: Which is the method of lives it's the most that is used for this revelation of ideas.
José de Jesús Padua Argüelles: And the ideas that was mentioned is too complex, if I everything and then suppose that I have an original integration control like this Gray line here.
José de Jesús Padua Argüelles: And I would like to be form it into a controller, that is not oscillating, if possible, and that is also as quickly converging as possible, but I will also like this the form control to touch the selling points of the action.
José de Jesús Padua Argüelles: so that I can still do semi classical approximations.
José de Jesús Padua Argüelles: I think also that such magical country exists it's called ellipses symbol and then simply our solution to this initial value problem in which the vector field.
José de Jesús Padua Argüelles: Is the minus the gradient of the real part of the exponent and then the initial condition is that as time goes to minus infinity i'm in the critical in a cell of the reaction.
José de Jesús Padua Argüelles: So in this case, it would be this Green Line so we have the original control and this West point, which is a critical part and then I see these green light is a solution to the flow that has initial condition being the the critical point.
José de Jesús Padua Argüelles: So now, the integration controlling which I will actually do the calculation, will be the symbol.
José de Jesús Padua Argüelles: which has a property that alone eat there's a constant imaginary part for the experience, so I don't house relations and then it disappears descent line for the real part so psycho away from the critical point then i'm yeah the.
José de Jesús Padua Argüelles: The absolute value of the integration is decaying as quickly as possible it's I mean it's doing so exponential.
José de Jesús Padua Argüelles: Here the system that i'm considering.
José de Jesús Padua Argüelles: depends on on on a parameter.
José de Jesús Padua Argüelles: And I can there is basically a boundary data of reaction and I see that if I change the boundary data from being positive in this case to negative, then the whole picture changes.
José de Jesús Padua Argüelles: So this is nice because i'm sort of having a generalized notion of the rotation in which I be formed the original integration control into something else that is convergent.
José de Jesús Padua Argüelles: But this will depend on the action and also in the boundary data, so I have some sort of dynamic that way to do.
José de Jesús Padua Argüelles: Week rotations.
José de Jesús Padua Argüelles: So this is the setup that we use and it's also served there was using the continuum before.
José de Jesús Padua Argüelles: Okay, so it's not loading the picture okay.
José de Jesús Padua Argüelles: So yeah Let me now apply these methods to.
José de Jesús Padua Argüelles: Our exponent.
José de Jesús Padua Argüelles: Because we have empathy throughout the.
José de Jesús Padua Argüelles: The original integration continuous correspond to having a big rotation angles by.
José de Jesús Padua Argüelles: And here i'm showing the the flow of the of the websites symbol in already there the analytically extended domain for five.
José de Jesús Padua Argüelles: And this is not completely analytically extended because I still have the these little riff ranch coats or Lorenzo in beta.
José de Jesús Padua Argüelles: And therefore, the original integration control can be either the whole line at file.
José de Jesús Padua Argüelles: If I include because of the regular region, and if I do so, I will need to choose.
José de Jesús Padua Argüelles: Which side over the branch good I associate to discuss on a regular bar.
José de Jesús Padua Argüelles: Or it can be just simply the regular part of deliverance and region okay.
José de Jesús Padua Argüelles: So, in any case, if I am to be form to the next at symbol, then I am to refer to these up them branch.
José de Jesús Padua Argüelles: any particular these up and branch has the opposite sign, then what happens with heartland surgeon Okay, so this is a so called villain insane and actually what I have is not exponential of minus the up an action but it's explanation of plus the up and action.
José de Jesús Padua Argüelles: Okay, so this is how we differ from Part one and i'm hoping, but I mean this is, this is not new, this is the discussion wearable also in the context of our lives, a theory by two broken February and only dollars.
José de Jesús Padua Argüelles: Okay, so we want to reform the symbol.
José de Jesús Padua Argüelles: If we are to exclude the regular region, then we have to connect.
José de Jesús Padua Argüelles: The lawrenson integration domain here to the thimble by adding a little Arc that starts in the end of the branch good and connects the beginning of the up and domain, so we will have to contributions to a particular one from this tiny are.
José de Jesús Padua Argüelles: And then one from the Euclidean.
José de Jesús Padua Argüelles: branch Okay, however, if I am to include the regular regions, then the only way I can be formed from Ethiopia, to me, is if I choose the right side of the branch good and therefore wanting to.
José de Jesús Padua Argüelles: Be forming to the feeble.
José de Jesús Padua Argüelles: chooses outside of the branches.
José de Jesús Padua Argüelles: And this, in particular, is opposite to the choice of of Luke on certain Okay, so these overall would be exponentially enhanced but because of this choice in this case, it will be exponentially suppressed Okay, so now it would be nice to see how these two.
José de Jesús Padua Argüelles: options differ and, in particular, how, how will do the approximate the continuum physics.
José de Jesús Padua Argüelles: And it or southern so here i'm showing this is a, this is a typo, this is the absolute value of the partition function okay what i'm saying in the lifetime.
José de Jesús Padua Argüelles: So in black i'm showing the contribution of the UTV in line and in great i'm showing the tradition of the arc that connects that there is no end to the up and branch, and we see that for large.
José de Jesús Padua Argüelles: Late scale factor.
José de Jesús Padua Argüelles: The contribution of the Act dominates Okay, and then in the left in the right panel i'm showing just the contribution of the European domain and the contribution of the continuum effective action.
José de Jesús Padua Argüelles: yeah actually so it's not the full continuum no action it's a continuum action that has to be tweaked so that we only have one critical point.
José de Jesús Padua Argüelles: Because the triangulation that we are considering does not allow I mean it only covers either the Ukrainian Ukrainian region or the low incineration region so we only have one critical points, so we have to manipulate the continuing action to have only one critical point.
José de Jesús Padua Argüelles: But we see that if I only consider the ATM branch, then I have a very nice approximation of this modified continue.
José de Jesús Padua Argüelles: Whereas if I include the Ark then this agreement will actually break for large values of the late scale factor.
José de Jesús Padua Argüelles: And therefore, the exclusion of the regular region region, seems to me to worst results okay so that's an important point, it seems that we should now include this region, but with the suppressing branch Okay, the overall suppressing branch.
José de Jesús Padua Argüelles: Okay.
José de Jesús Padua Argüelles: So.
José de Jesús Padua Argüelles: yeah I also have the results for the case in which.
José de Jesús Padua Argüelles: The because here they Shell in the lawrenson to lawrenson case so boundary data is used Miller answer to answer.
José de Jesús Padua Argüelles: Any in this case.
José de Jesús Padua Argüelles: The symbol is this lining green and we see that.
José de Jesús Padua Argüelles: It actually approaches that you premium brands, but now what five equals zero so in this case we actually recover.
José de Jesús Padua Argüelles: The exponent being men's the exponential action, yes i'm.
José de Jesús Padua Argüelles: Sorry, the the explanation of the action in the attorneys are, in this case the team will go through the branch cooked.
José de Jesús Padua Argüelles: And then goes to another up on branch, which is an analytical continuation and different analytical continuation from the enemy, that does not really reproduce up and geometry.
José de Jesús Padua Argüelles: But again, the feeble will choose over at suppressing sides of the branch goes, so this.
José de Jesús Padua Argüelles: In this first picture, which is before I analytically continue through the ranch codes.
José de Jesús Padua Argüelles: And I mean the right of the branch good, which will be the suppressing choice, and then I cross the branch good, but when I cross it I do the analytical continuation So although i'm now in the left side of the branch good it's been over and suppressed.
José de Jesús Padua Argüelles: And this is actually something that we expect on general terms when we have a lawrenson critical point, because if they've already got a critical point is a critical point is in the regular region.
José de Jesús Padua Argüelles: Then the real part will be of the of the exponent will be zero and following the flow will make it negative, so we will have something to suppressing.
José de Jesús Padua Argüelles: So.
José de Jesús Padua Argüelles: that's that's other easterlies cosmological model and therefore let me conclude.
José de Jesús Padua Argüelles: And summarize but, but essentially.
José de Jesús Padua Argüelles: I told you about.
José de Jesús Padua Argüelles: Some notions about crossing the complex reaction.
José de Jesús Padua Argüelles: motivation for these is to be able to compete real time intervals.
José de Jesús Padua Argüelles: Methods for these are the lecture symbols and yellow Murphy great for metals, both of which required to complete SCI fi everything.
José de Jesús Padua Argüelles: And, in particular the surf complex rejection also allows us to consider a unified framework for mixing signatures.
José de Jesús Padua Argüelles: And the main motivation for this is to understand each unit integration range in this sort of reggie like.
José de Jesús Padua Argüelles: I think.
José de Jesús Padua Argüelles: we've also tested the topic of clinical psych evaluations and spatial topology change and asked whether this should contribute or not to the path, integral and all the previous results and other approaches say that they should not.
José de Jesús Padua Argüelles: With yeah we have reasons to believe that, because you unless it symbols provide some mechanism so that these will always be suppressed, and therefore they can be included.
José de Jesús Padua Argüelles: which would improve numerical efficiency, because then the test to see whether something is scarily regular or not, does not have to be to be done, and this, this is hiding on local so we would replay.
José de Jesús Padua Argüelles: America power.
José de Jesús Padua Argüelles: And with this yeah I mean the question is still open, which configurations to run some over in Lawrence empathy circles and, in particular in this particular instance I think events, which is where this Castle a regular regions are kings causality valuation can appeal.
José de Jesús Padua Argüelles: And it would be interesting to me to will apply this to to effective sniffles we are close to these kind of rigid quantum reggie countries that we consider.
José de Jesús Padua Argüelles: But even more so to understand whether this type of hints causality violations can appear in the seo tactics of of speed forms.
José de Jesús Padua Argüelles: And yeah okay that's that's all I wanted to say, thanks for your time.
José de Jesús Padua Argüelles: open for questions.
Abhay Vasant Ashtekar: asked me to take over so.
Abhay Vasant Ashtekar: That that questions so you can just.
Abhay Vasant Ashtekar: raise raise your hand or.
Abhay Vasant Ashtekar: yeah.
Abhay Vasant Ashtekar: So don't y'all y'all raise your hand so, can you go ahead.
Suddhasattwa Brahma: hi so yeah my question is in two rocks calculations, they find that the perturbations make this whole scheme.
Abhay Vasant Ashtekar: fall down right.
Suddhasattwa Brahma: So there's come with inverted options and the permissions are run away, did you look at perturbations in your case, do you have any hints for those.
José de Jesús Padua Argüelles: No, no, we we haven't considered that.
José de Jesús Padua Argüelles: I don't know how to add, I think the matter in the paper, I think.
Suddhasattwa Brahma: We know that in fact even not.
Suddhasattwa Brahma: I mean just for 10 sermons also so if we just have cosmological concert just for the tensor model, you have runaway perturbations.
José de Jesús Padua Argüelles: yeah I mean we haven't thought of that, but we are sort of taking the their notion of.
José de Jesús Padua Argüelles: You know, defining this putting two girls in the leadership team.
José de Jesús Padua Argüelles: So we can see that to be in this approach, more fundamental so I guess, we should be in agreement with them because that's kind of the.
José de Jesús Padua Argüelles: There yeah.
So maybe just.
Suddhasattwa Brahma: Maybe just a related question, and maybe you have mentioned this, but I missed it so what when does your integral run over so does it go from minus infinity infinity for the left or from zero to infinity what is the.
Suddhasattwa Brahma: order that.
José de Jesús Padua Argüelles: It goes from zero to infinity.
Okay yeah okay.
Suddhasattwa Brahma: Thank you.
Abhay Vasant Ashtekar: yeah ding ding your question.
Ding Jia: Yes, thank you.
Ding Jia: Nice talk.
Ding Jia: I have a question there's a point you mentioned you compare your results with number know the boundary proposal, the continuing yes and you say, if you include the irregular part things agree and.
Ding Jia: Better.
Ding Jia: yeah, how do you understand the continuum result.
Ding Jia: To you, do you think that they are not including the irregular configurations the continuum bath and the girl yeah.
José de Jesús Padua Argüelles: So I think it's kind of tricky because in the continue this kind of hints cause any violations do not appear.
José de Jesús Padua Argüelles: At least.
José de Jesús Padua Argüelles: yeah I mean the, the only way, something I could picture something like that appearing is no.
José de Jesús Padua Argüelles: Yes, maybe an atrocity like space, then I guess, but the way we're doing the comparison is like a seeing this transition and pieces here.
José de Jesús Padua Argüelles: So yeah we can perform this potential, but he, as I mentioned, we have to trigger on this a little bit to to recover only one critical points.
José de Jesús Padua Argüelles: And the way we do this by dropping these to return.
Okay.
José de Jesús Padua Argüelles: And yeah in this case we miss you have the Euclidean so if we consider just the theme.
José de Jesús Padua Argüelles: And therefore, include the irregular region, then we have a nice agreement, but we see that if we are to include to exclude the regular region, then we need to add the Ark.
José de Jesús Padua Argüelles: And this will dominate for for large.
José de Jesús Padua Argüelles: seconds scale factor.
José de Jesús Padua Argüelles: And it will actually exponentially, you know, in it, because he said look loss, and it will ruin this kind of approximation in.
José de Jesús Padua Argüelles: game in the right picture.
Ding Jia: yeah what I want under some better is a is this sort of.
Ding Jia: confusion, because it seems the continuum result there actually is a.
Ding Jia: is real and their path integral exponent is imaginary over here in your case you have complex exponent with both real and imaginary part isn't correct.
José de Jesús Padua Argüelles: No, in both cases, it will be so if I when I do the information it will be a real exponent and therefore we are resolved.
José de Jesús Padua Argüelles: But yeah So if you will, this lefsetz symbol method to this modified continuing action, you will find that the symbol is actually again just the Euclidean line with the branch that gives me last up an action.
José de Jesús Padua Argüelles: And yeah that's that's how we compete at putting together and it gives you something real because, because when I do, that information I can and its benefits to that and we get something we elephant so.
Ding Jia: And then.
José de Jesús Padua Argüelles: Does that.
Ding Jia: Understanding you.
Ding Jia: The original in the continuum the original bass and do is defined in the lorenza then they so in the original I think to grow.
Ding Jia: The exponent is purely imaginary Is that correct.
José de Jesús Padua Argüelles: yeah it's great.
Ding Jia: and your case that the discrete model, the original path into grow.
Ding Jia: As an exponent that's complex that is both imaginary and real parts Is that correct.
José de Jesús Padua Argüelles: Yes, yes.
Ding Jia: So it seemed the in the original domain there's some difference between the two definitions and it surprises me that when you after you do form them the results agree well.
José de Jesús Padua Argüelles: yeah yeah I guess yeah so depressing but.
Abhay Vasant Ashtekar: yeah I guess it really.
Abhay Vasant Ashtekar: Does because what dominates it's the same same thing.
Abhay Vasant Ashtekar: Exactly yeah you're calculating certain approximation, you know, mainly, and then the dominant contribution is following the same path is the reason why you're getting agreement.
José de Jesús Padua Argüelles: yeah yeah I would yeah that's how we put it yeah and.
Ding Jia: Then the question is for the discrete model, you can choose an action as purely a real and the exponent is purely imaginary after you do the different motion was it still the same park dominate why, why is it different.
José de Jesús Padua Argüelles: Now, but.
José de Jesús Padua Argüelles: I can you read the question.
Ding Jia: There there's a if you do not include the regular parts.
José de Jesús Padua Argüelles: Yes.
Ding Jia: you're discouraged model, you have Lorenzo in theory, when you when you do the deformation compute the result it disagrees with a new one, and if about his reasoning, a fellow that reasoning should not expect the same result because the same same thing that dominates.
José de Jesús Padua Argüelles: Nobody in that case the other thing with dominant because I have these additional contribution from the UK.
Ding Jia: which comes from your regular space time configurations, which is not included, it seems like continue.
José de Jesús Padua Argüelles: yeah yeah it's not included, but in order to connect to the.
José de Jesús Padua Argüelles: To the thimble I need to have this Arc.
José de Jesús Padua Argüelles: And they.
Abhay Vasant Ashtekar: are fine yeah that guy's a point that seem a little bit of confusion, because you have to do something and just continue limiters taking us.
Abhay Vasant Ashtekar: New ways which is not most direct it seems to me.
José de Jesús Padua Argüelles: yeah.
Abhay Vasant Ashtekar: And I think that is also doing is saying is that thing that that's what you're saying.
Abhay Vasant Ashtekar: In the continuum limit somehow you know you said, well, I do.
Abhay Vasant Ashtekar: something you know, otherwise I will not get agreement.
José de Jesús Padua Argüelles: yeah yeah yeah Of course I mean yeah I see the issue, but you know we needed to compare with something and that's, the best thing we came up.
Abhay Vasant Ashtekar: Against.
Abhay Vasant Ashtekar: You can again see what it what exactly you did yeah you tweak the continuing action somehow So yes, what do you do.
Ding Jia: yeah, I guess, this is a question is not asking for answer, but just wanted to throw it out So how do we interpret those as a result, should we say that the continuum result is correct or the discrete result is correct, because.
Ding Jia: there's a reason to to say we shouldn't include the regular configurations.
Ding Jia: Because during the regular and I think we shouldn't take it for granted that whatever agrees with a continuum is correct.
Ding Jia: comment.
Okay.
Abhay Vasant Ashtekar: I think they didn't can we come back to this question because.
Abhay Vasant Ashtekar: I hadn't submitted confusion and so on, but, but I think hand is raised his hand so let's ask her how to speak first and then we can come back to this question.
Hal Haggard: I don't mind if you stay on this question because mine was in a rather different direction.
Hal Haggard: and very nice tacos a thank you in particular, I enjoyed a lot your your treatment of the the day he drill angles in the in the warranty and.
Hal Haggard: And somehow you've done the clearest job i've seen of the analytic continuation, but even so it's a total mess right there.
Hal Haggard: The day you drill angle functions are complicated and you have to keep track of these choices and then.
Hal Haggard: You know, and I think you're you're giving nice logic, you know, looking at whether.
Hal Haggard: These causally irregular configurations are suppressed or not, but i'm wondering if you've thought at all about a simpler principle that might pick out.
Hal Haggard: A good choice of day he drill angles that doesn't have to go all the way to the end of the calculation to see which choice was a good choice does it make sense, what i'm asking.
José de Jesús Padua Argüelles: yeah yeah It makes sense um.
José de Jesús Padua Argüelles: yeah I guess the most up a priori argument that I can think of this this argument used by by certain which is.
José de Jesús Padua Argüelles: You know, we went through officers to be surprised.
José de Jesús Padua Argüelles: But then yeah another yeah, I guess, one can define your instant angles and other way.
José de Jesús Padua Argüelles: Which is.
José de Jesús Padua Argüelles: You know I can so if I have again this picture of having a which connecting the first and the second quadrant a good to do something like reflect the first right into the second and then again just this notion of the of the arc of the of the the length of the arc.
José de Jesús Padua Argüelles: And then maybe say Oh, you know, can I can I make this additive somehow.
José de Jesús Padua Argüelles: And I believe this is actually related to this certain definition of the angles, and it will be purely real but then there's this claim by sorting saying that if one wants to reproduce I think Gospel name, because when a few and also like.
José de Jesús Padua Argüelles: To look at it is to to translate from me up into one cohesive and you have to introduce complex angles.
José de Jesús Padua Argüelles: And in that case yeah the first yeah like.
José de Jesús Padua Argüelles: The most direct or you know the most like a priori reasoning that I can come up with with the this this profit prospecting.
Bianca Dittrich: Maybe to school in a question to two people going to flow in and comment about spin forms.
Bianca Dittrich: spin.
Bianca Dittrich: spin forms for the analytical forces me classic limit to not use the finishing of the heater england's.
Bianca Dittrich: You define an anger, but typically just for space like tetrahedral but it's only the sin is, if you consider sandwiches and white patches.
Bianca Dittrich: and have different formulas for these two cases, but you do not have an imaginary part and then you define the deficit in again just as a some.
Bianca Dittrich: So by construction you don't have any imaginary part but this version does not satisfy the Gospel nice human and 2d so there might be something missed in this discussion.
Bianca Dittrich: it's it's a bit unclear in.
Bianca Dittrich: What happens with his contribution and informs.
Bianca Dittrich: And furthermore, also this is ambiguity, if you are a few analytically continue this ambiguity disappears in the sense that you do get to equivalent definitions.
Bianca Dittrich: Maybe that was your question.
Hal Haggard: Well there's still the the the overall sign choice right, even if.
Hal Haggard: Even if you do the analytic continuation, am I wrong.
Bianca Dittrich: There is an overall sign choice whether.
Bianca Dittrich: We did this just in the labs and then finally it's the quotation English, you can extend from zero to four pie.
Bianca Dittrich: And so you get these different versions of circadian excess intervention exits now, if you want to do pecan left shirts it's important to get it.
Bianca Dittrich: Because he also also into workspace and here we have seen that cleaning regime, you get one sign for 13 X, I mean we get need to take to one side.
Bianca Dittrich: And so what's the quotation in one direction.
Bianca Dittrich: and for the other choice, if you and there's laurentian regime, we need to be quoted in the in the opposite direction.
Bianca Dittrich: So you need that freedom to get convergence.
Bianca Dittrich: And in fact.
Bianca Dittrich: There was also a question or pseudo it's kind of a dynamic dynamic a way to deter mine.
Bianca Dittrich: And more complicated version of the quotation, and so we expect if you add perturbations you shouldn't really think of set expectations, but you should include the non perturb actively ideally and repeaters analysis in which direction you week what Kate.
Bianca Dittrich: And so, in some sense soaking and Lupo considered as a Meta fields, they did not consider the geometry, they did not integrate over geometry degrees of freedom.
Bianca Dittrich: And so the Meta theory is it to something opposite to the geometry design, which actually is not surprising, because these two terms content out and the hamiltonian constraint.
Bianca Dittrich: And so what one should do and principles to put everything together and and look for basically whereas this integrated convergence and so What it does is also to ensure that that you pass it that you can actually compute the possibilities that are gorgeous.
Bianca Dittrich: And that could be one mechanism to.
Bianca Dittrich: To to address this issue as a presentation and john locally analysis and also mechanism that just kind of complexity fine, even though.
Bianca Dittrich: Initial data in some sense.
Hal Haggard: thanks for the comment.
Abhay Vasant Ashtekar: Okay, so we can go back to this this other question that did was, I mean I think many of us what is not clear is.
Abhay Vasant Ashtekar: What is the kind of what what is a.
Abhay Vasant Ashtekar: At the end of the day, what can we say we achieved by going to the discrete and you know in some sense, one can take it to the well going to these discrete disk utilization so on just because I don't know how to do the contingent particular.
Abhay Vasant Ashtekar: But then, and then.
Abhay Vasant Ashtekar: Various people.
Abhay Vasant Ashtekar: leaner and draw console and I told us how to do it, so what is it that we are learning, which is about what they told us, and why should we trust one thing more than another that I think the general gist of digs question.
yeah.
José de Jesús Padua Argüelles: yeah I mean I find interesting these beings point.
José de Jesús Padua Argüelles: Of Okay, maybe we should think of very good at something more fundamental and then.
José de Jesús Padua Argüelles: Then, maybe we should add the they really like contribution, after all, but I yeah I mean the way I think of of.
José de Jesús Padua Argüelles: Of what i'm trying to say is know that we're trying to recover something from the screen, that we cannot have in the continuum.
José de Jesús Padua Argüelles: it's more on trying to understand how to be with infinity integration ranges in the in the script and also with this Castle irregularities or hibiscus tea violations.
José de Jesús Padua Argüelles: So it's more in the sense of how should we do path in regards to the street and not really, what do they discrete tell us about.
Abhay Vasant Ashtekar: That so when when you want to do that, however, I because again other people have pointed out hollows pointing out that you know what exactly you mean by dial angle and saw.
Abhay Vasant Ashtekar: There is complicated.
Abhay Vasant Ashtekar: And so, one has to make some definitions and in one can argue, is that it is natural somebody else might have you some other data is natural.
Abhay Vasant Ashtekar: So basically the inputs that went into.
Abhay Vasant Ashtekar: discrete calculation, so I mean just one can say that well, maybe your final results are ugly our reflection of the inputs that you mayor.
Abhay Vasant Ashtekar: yeah and so you know with other inputs will get some other answer so if you take this greatness as being a fundamental thing.
Abhay Vasant Ashtekar: Then I mean if if you took this greatness has been phenomenal thing and then you had no inputs to be made, then everybody would be happy, but if there are inputs to be made, also, that one would just say that well and it's.
Abhay Vasant Ashtekar: it's more like saying that if I do do this, then I get this, but other than visits physically more fundamental I bake playing devil's advocate now obviously appreciate very much what your top.
Abhay Vasant Ashtekar: But I just wanted to sort of play the devil's advocate obviously isn't, namely know what the external Community will say.
José de Jesús Padua Argüelles: yeah.
Bianca Dittrich: I mean if I, if I can comment so here's The first point is that if you try to really do logins and passwords says actually many, many decisions.
Bianca Dittrich: which you have to make to define what you actually fund since antenatal one.
Bianca Dittrich: And that holds to some extent, also on the continuum because you can construct thousand configurations or something.
Bianca Dittrich: And we would have to this no, you can also consider can signature change changes and pitino it goes to.
Bianca Dittrich: So far, if you if you're on the matrix report.
Bianca Dittrich: How, how do you actually enforce invented signature or not so indeed year by the invoice to consider cosmology and initially we didn't expect anything.
Bianca Dittrich: Like causality violations but it's something which you also get generically and we didn't consider as a question, you know when the integrated over.
Bianca Dittrich: You have two choices actually see choices.
Bianca Dittrich: equals one is to exclude the regular reaching the other two were kind of left to hide from the punch card to suppressing was it is enhancing pilot and so.
Bianca Dittrich: Is it is, if you if you do exclude the regular region, you get something which is slightly different from the continuum or in this case quite a bit different from the Aquino and if you choose so pricing side you get quite a good agreement.
Bianca Dittrich: And if you choose enhancing site you get something on sensitive.
Abhay Vasant Ashtekar: So what might just say that one is learning something about the disc.
Abhay Vasant Ashtekar: How to how you should do discrete ization properly and not so much about continue again i'm taking payments.
Bianca Dittrich: NDP we agree that one should.
Bianca Dittrich: Consider more examples and possibly also kind of more dynamic topology change itself it's which which we started to be.
Bianca Dittrich: able to learn something there actually is a digitization heads, because it allows you to construct these things a bit easier than.
Bianca Dittrich: and continue.
Bianca Dittrich: But first aim of of this was to actually do first, first of all top us integrates.
Bianca Dittrich: kind of numerically facing the problems that you have an infinite.
Bianca Dittrich: infinite integration range.
Abhay Vasant Ashtekar: But is that funny, why did you enough I I typically just look at the the dominant parts right the what is now on the slides here.
Bianca Dittrich: No, no, they really.
Bianca Dittrich: Do we know why we numerically that's the difference to to to have it all in numerically integrated.
Bianca Dittrich: Always in control plus parts, but you need to connect to the virtual country.
So it's really.
Bianca Dittrich: it's.
Abhay Vasant Ashtekar: Somehow it was this was not clear to me.
Maybe.
Bianca Dittrich: it's an exact evaluation of the positive.
Bianca Dittrich: This you know this is this is two choices and the message is indeed at least here you have punch card, and you have to make those choices.
Abhay Vasant Ashtekar: Okay ding do you have for the questions.
Ding Jia: Those are adult.
José de Jesús Padua Argüelles: Okay.
Abhay Vasant Ashtekar: Any other comments or questions.
Simone SPEZIALE: Yes, the just a quick comment and maybe a quick question to comment was, I think bianca was mentioning whether these these imaginary shooting steam forums and.
Simone SPEZIALE: At least I would say, there is a possibility that the shift existing as painful as as well, because when we look for laurentian critical points.
Simone SPEZIALE: The result is not a pure boost for the alanna me but there's always also rotational pie, that is exactly give them by time digging into account whether it's a thick wedge or thin which and these you can interpret in the end, as being a.
Simone SPEZIALE: shift of the angle of the booster by an Ai pie, so, in fact, even in the US into the formulas, you have things like some over pies or we need equations you have so I don't know it was just a common he's related to what bianca is.
Bianca Dittrich: After that's that's very interesting.
Bianca Dittrich: Because I was looking for that.
Bianca Dittrich: I was looking for that, so it will be good to clarify that it seems as important formulas people always use this in batch and and.
Bianca Dittrich: And it's not.
Simone SPEZIALE: Really, you.
Simone SPEZIALE: You remember this, these minus one to the number of thick wages formulas for renting.
Bianca Dittrich: out so.
Simone SPEZIALE: So, if it is interesting, then we can discuss and I can tell you where it comes from.
Simone SPEZIALE: And the question is, I guess, in these integrations you're doing it, the measure is just a somehow trivial major over the excellence right and I was wondering whether busy regular configurations could be.
Simone SPEZIALE: surprised if one introduces some suitable measuring or kind of like in causal dynamic of regulations that there are some other types of irregularity, but then those are the types that can be dealt with, with the measure changes.
José de Jesús Padua Argüelles: So yeah thanks thanks for the question of the measure so yeah we're kissing dimensional coming from the.
José de Jesús Padua Argüelles: yeah inspired from the continue so here, then you continue to enjoy your thing something like this and the measures that we can seeing will be you know.
José de Jesús Padua Argüelles: there's something like the one of the spirit of the height.
José de Jesús Padua Argüelles: But yeah I mean we have not thought about the measuring somehow dealing with a castle a regular progress.
Simone SPEZIALE: And I remember the bianca used to say that they were better choices of measures that would come from you know environments under partner moves, for instance, could these also affect.
Simone SPEZIALE: Because you're losing it, you know, usually in the career path approximation, you know.
Simone SPEZIALE: shouldn't matter so much to measure because you're looking at regular points these might be such that they measure zero or the Virgin there and then my matter so that's why i'm asking this kind of question.
José de Jesús Padua Argüelles: yeah yeah it's it's a nice question, yes, something nice to think about.
Bianca Dittrich: Okay, if you, you know the single most popular move is to go into the find more and actually also decides to measure.
Bianca Dittrich: If you will find more we expected to contributions or says regular regions will be will be less than some sense and because this kind of problem it's kind of related to one pound of covenant.
Bianca Dittrich: component and descriptive patients.
Bianca Dittrich: But it's not clear whether we should sing a physical and spin forms, you can actually do this continuum limit in the space, you have to speak, by us always encounter these contributions and then cdt indeed these configurations are explicitly forbidden.
Simone SPEZIALE: Right.
Simone SPEZIALE: So they.
Are.
Bianca Dittrich: kind of explicitly forbidden.
Bianca Dittrich: And that's.
Simone SPEZIALE: Also, something like invariance under the one five move will give you more constraints on consistent gluing and, therefore, then measure me suppress or yes, the reason for that.
Bianca Dittrich: No, I think, considering something like.
Bianca Dittrich: In weapons and, as he moves.
Bianca Dittrich: and actually even just considering 3D would tell us whether to include these retreats or not.
Bianca Dittrich: So adjusted people haven't studied that at all and insert signature.
Bianca Dittrich: So in fact.
Bianca Dittrich: That said, already Taylor tells us that we should, for instance, include these are three different set of points.
Bianca Dittrich: Because that you get just from an element and moldings and millions of one five minutes.
Abhay Vasant Ashtekar: But along the same lines, there is a.
Abhay Vasant Ashtekar: This whole analysis, starting from talking to lainer to rock etc to what you are doing now, I mean one focusing just on the.
Abhay Vasant Ashtekar: Transition service amplitude to go from one classical configuration to another classical configuration, but of course in the farmers all word which led to part integrals he was really.
Abhay Vasant Ashtekar: Asking for transition amplitude, for you know for for content, one given quantum state to another state.
Abhay Vasant Ashtekar: And that requires a Gilbert space i've been coming States now in spin forms and look on gravity, we have that in our space.
Abhay Vasant Ashtekar: But in this case is what never talks about what the major is on the on the configuration spaces.
Abhay Vasant Ashtekar: And so to me it's always very, very incomplete because i'm not asking a physical question answers to physical questions were quite different if you know if you have the.
Abhay Vasant Ashtekar: Correct physical measure here what is now Yulia shouldn't also in Wellington prescription I believe nivea assuming that the major it just you and, by the way in Asia scale factor so si si si D.
Abhay Vasant Ashtekar: That is clearly not a good measure.
Abhay Vasant Ashtekar: Implicit assumption one wasn't.
Bianca Dittrich: I mean i'm not sure what you're referring to the measure and the continuum is constructed by doing by doing a variable transformations and you get a quadratic integrator.
Abhay Vasant Ashtekar: Can you do this, no, no that's a major.
Simone SPEZIALE: Nobody means there's no is that I can only carry this piece for the boundless.
Abhay Vasant Ashtekar: Because interested is really the.
Abhay Vasant Ashtekar: Reason an ambiguous between.
Abhay Vasant Ashtekar: States not been in classical.
Abhay Vasant Ashtekar: configurations because classical configurations for an independent thing right it's not.
Abhay Vasant Ashtekar: So, therefore, the whole questions that.
Abhay Vasant Ashtekar: You know, people are talking.
Abhay Vasant Ashtekar: Later, to rock etc answer ask that really missing a very, very critical point issue is that not physical questions that weren't asking looking just as going from 181 of a I I can you know change my.
Abhay Vasant Ashtekar: The classical configuration space, as I want, I mean the major the content will work spaces very, very important, which is somehow not.
Abhay Vasant Ashtekar: i'm not asking this that therefore, you should do something right away, but to me this is kind of an important open issue, which is sort of an elephant in the room, which is just ignore it.
Abhay Vasant Ashtekar: Okay okay that that was the last question that Laura.
Abhay Vasant Ashtekar: Laura is not obviously don't ask it or not, because I think.
Laurent Freidel: It was more it was more remark.
Laurent Freidel: When will was remarks One was about the question you were asking it is consideration, I think I think there's a context in which yeah, we need to resolve the situation and there's much more to it than what.
Laurent Freidel: A true rock and dinner has been doing, you know they've been doing, you know think left hand symbol in the context of quantum theory been quantum theory you're not allowed.
Laurent Freidel: To have the ability to change, in fact, you know we don't know what are the rules of extension for that.
Laurent Freidel: And once you have a proposal for quantum gravity ability to transcend, since this is maybe where quantum gravity can come in it's to to resolve what is, what is the physical prescription for.
Laurent Freidel: For quantum gravity amplitude with battery states that may you know may have no classical configuration and and so that's where you know being discreet, you know, bring something.
Laurent Freidel: New another example where in fact it happens it's in the context where we do exactly know what is the quantum gravity amplitude it in 3D quantum gravity.
Laurent Freidel: And there you know another column very gently to the selected by the argument of symmetry and there you can really show that, if you take at least the local way to take a local way to be such that the battery states.
Laurent Freidel: violates, for instance, the the triangular inequality, it is exponentially suppressed that's that's a consequence of the political environment or different environments for the amplitude.
Laurent Freidel: Now, with with you know you're doing here is trying to see Okay, what happens with this exponential suppression, when you glue different amplitude but anyway, I just wanted to emphasize that that this is where quantum gravity bring something new that quantum theory does not have.
Abhay Vasant Ashtekar: rocky I agree with you, but not completely because I mean yeah miss anyone does talk about.
Abhay Vasant Ashtekar: amplitude to survey data by instant transfer example, who changed now, instead of space time topology topology the field exactly you know.
Abhay Vasant Ashtekar: So, so, so I think what one does input included katie one does have that that can okay.
Laurent Freidel: So it's not the not.
Laurent Freidel: The not.
Abhay Vasant Ashtekar: The space time.
Laurent Freidel: And I failed and Luke oh that's that's what they attempt to do in 2d and and it's confusing, so the attempted to have a prescription for space time to produce a change in the continuum but that leads to other you know.
Laurent Freidel: But in the dispute, you have that more much more under control.
Bianca Dittrich: So positive messages, indeed, and if, if you are interested in this question should include properly to change or not, it just that there's no mention in the momentum and the.
Bianca Dittrich: setup in the discreet and continue you encounter that quite often.
Bianca Dittrich: and pick I left a message and printed the case you seem to tell you that these configurations can be always suppressed.
Bianca Dittrich: And that's a new point as compared to to sorkin's description variety your eyes are suppressed one choice, but have to enhance your choice.
Bianca Dittrich: Which to ask him to be always dangerous and the example to be so wasn't physically physically reasonable, so the positive news is possibly you can include these things and they're all these suppressed, you might also try to exclude them.
Bianca Dittrich: would be however non local constraints and so on, so that might that might be just also kind of quite a lot harder to do and it's something which we haven't actually discussed yet so that would who ended the election of cvt like your pores explicit.
Bianca Dittrich: Because energy constraints, but it's good that you can compare these two choices and that there is a choice, possibly, they can they all these things I actually suppressed.
Abhay Vasant Ashtekar: Right, I think it's all been 35 minutes, so it would you call it quits and thank you very much for the seminar, and thank you very much for the discussion okay bye bye.
Bianca Dittrich: Thank you.