Jorge Pullin: Okay, so our speaker today is going to be charging penny, who will speak about how it was magical constant cuneiform surgeries and LPG.
Qiaoyin Pan: Thank you.
Qiaoyin Pan: Everyone thanks for the introduction and thanks for giving me this opportunity to present my work here.
Qiaoyin Pan: So yeah today i've talked about the customer to constant couple with the model El que je and see how it cutie forms the signatures, there is based on the work in collaboration with Valentine bouzou mighty duties and rollins to me.
Qiaoyin Pan: The current standard model of cosmology, together with the data tell us that the customer to a constant hasn't non zero value.
Qiaoyin Pan: is very smallest, so this motivates us to generalize the models of contracting with the zero COs module constant wonder, that is to build the curve geometries implied by generativity by quantum discrete building blocks according to certain own graphic theory.
Qiaoyin Pan: And in recent years, yes, been claimed that we can use curve drama cheese as a building block.
Qiaoyin Pan: When we include a customer's account constant so that we can better approximate the continuous theory and we hope that you can help us to solve the dynamics better.
Qiaoyin Pan: This idea has been used in, for example, these these these work, so now we want to apply this idea to 3D quantum gravity theory with a non zero on.
Qiaoyin Pan: The reason we want to work on 3D one body is because it's a topological theory, so it provides us a simple system.
Qiaoyin Pan: And it can provide us our guidance to understand for the contracting with unknown serial number, which is a more complex face more context system and it's still not well understood yet.
Qiaoyin Pan: Well, look on 3D it's a it's suggestive from, for example, simple, more inconvenient organizations model that.
Qiaoyin Pan: corner good structure the Pier when alumnus non zero, and it appears as a defamation of the frak case when a London is zero, for example in the speed for model when.
Qiaoyin Pan: London No zero or we get it to review a model as which can be viewed as the formation of the console region model for the London zero and in a controlled mandatory colonization when the alumni is not zero the quantum so mature group is cutie formed.
Qiaoyin Pan: As another approach to 3D look on gravity is gives a canonical formulation which your magically he represented on 2d discrete flat geometry for the canonical service in its kinematics and he described that the extremes curvature by growing this fat geometry together to be a 3D box.
Qiaoyin Pan: And to construct the.
Qiaoyin Pan: US you too embarrassing absorb was the 2 billion us is the spinners because they leave in the spin one half, which is the smallest MySpace so we can use them as the elementary variables to construct these observable.
Qiaoyin Pan: So this model and these two are for the fat case the London zero case, the question is, can we find a different version of it so that it describes the curve georgie.
Qiaoyin Pan: So these form the goals of this talk of the work that is, we want to construct a 3D before mtg model for the non zero on that from the canonical conversational approach.
Qiaoyin Pan: Such that the quantum crew structure will appear, naturally, you will also see in such a model, the.
Qiaoyin Pan: encodes them curve geometry, both in the editing medical and dynamic all levels and what did you build the absorb those with some before notion of quantum spinners that is encoded that is defined in this form, equity model.
Qiaoyin Pan: So in this talk, I will first described the chemical structure of this before model.
Qiaoyin Pan: Most a first at the classical level and the CD it's containerization it can be described by polonium fluxus or it can be described by espn or reputation and in the second part of describe the dynamic because structure of this different model.
Qiaoyin Pan: or relevant mathematical structure in its content model is quantum group also called algebra you can assume.
Qiaoyin Pan: it's used in the simple model where we consider Euclidean signature and this parameter the formation parameter Q can be decaying can be taken to be a real practice parameter, or it can be taken to the.
Qiaoyin Pan: As a rule of unity, but it's real it corresponds to a negative from the when it's a rule of unity corresponds to a positive number, and in this latter case.
Qiaoyin Pan: You can see two is the positive of algebra so in this case, we need to be more careful in the in the construction so.
Qiaoyin Pan: And in this talk, we will specialize in the simple in civil case when the q3 so that's setting, we will construct will specialize in the case of Euclidean switcher with a negative because much a constant, in which case the isometric group is going by so to see before that, let me reveal.
Qiaoyin Pan: The faith based structure the loop on the loop Bradley Facebook structure when alumni is zero the face space is described by the potential of you as you to order point car group which can be decomposed into an SDI.
Qiaoyin Pan: Crop semi cross product with our three and a basic variables given by the Columbia described by a CO2 and a flux described by the art three.
Qiaoyin Pan: We have to equivalent ways to describe the basic variables, either we use the lead momentum or right momentum which, for the fluxus and least two equivalent ways are related by am by X you to action on this process.
Qiaoyin Pan: rather call you can assign the hollow enemies on a link and a sign of success on the two ends of the link.
Qiaoyin Pan: and enter the focus when alumnus negative.
Qiaoyin Pan: The face face can also admit a decomposition or we use this, he was so decomposition of seo shoot.
Qiaoyin Pan: It to compose this Su to in sorry it could be composed this so to seep into Su to buy products product with an empty group to keep a notion of the formation, so we use this as you to stop group to describe the whole army and use the angels approach to describe the flux, so one.
Qiaoyin Pan: new feature of this.
Qiaoyin Pan: Next week or so much a constant case is the fastest corrupt from our three FLEX to an A into flux.
Qiaoyin Pan: We can also describe the faith based in to equal waste which corresponds to use your left or right momentum for the fluxus and they are related by a.
Qiaoyin Pan: As usual action what's new here is that we also have a back action of the boxes on the holidays, so in this two ways we have two different hollowness here.
Qiaoyin Pan: That means graphically we can stick on this, we can stick them this link into a ribbon so that work for side of the ribbons and we can assign these four variables on the on on the side of the River.
Qiaoyin Pan: The puzzle structure of this face space can be determined by a so called costco or images which is in built in the mathematical subject called the I Heisenberg double.
Qiaoyin Pan: Although i'm not giving the detail of this of the Heisenberg the bow and we just mentioned that this classical or matrix can be written with the generators of the two subgroups so when, in the lumber neck to pace, the cosmological calls and can be encoded in the into generators.
Western LQG Group: It sorry.
Western LQG Group: Can you can you say what is explicitly there and to group.
Western LQG Group: So.
Qiaoyin Pan: In a formula or of station can represent it as a lot triangle.
Qiaoyin Pan: A matrix with the diagonal elements given by real brighter and off diagnose him by complex variable and is determinant is one.
Western LQG Group: Thank you.
Qiaoyin Pan: So when we consider that graph in the flat case we have two sets of first class constraints mainly that coulson strength written with the fluxus and a flatness constraint with them with the Su to.
Qiaoyin Pan: wheel can also write a condition relating the left, right momentum as a second toxins constraints, then when we consider the default default a space.
Qiaoyin Pan: These notions can, firstly, that this graph, as I said, we can stick in all the links into ribbon so all we get is the soda ribbon graph here.
Qiaoyin Pan: And these notions of constraints can all speak deformed and what's very nice is in this when we.
Qiaoyin Pan: Have the when we encode these constraints in the ribbon they can all be represented as the trivialization of loops.
Qiaoyin Pan: And here, this is the condition requiring the tree, the two two ways to send a faith based or equivalent is what we call the ribbon constraints as the herbs and the closed loop of the ribbon and some.
Qiaoyin Pan: Similar to same as the fat case this new costumes during a flatness constraints are still first class and they generate the default Su to.
Qiaoyin Pan: Face transformation and the functions like translation, respectively, this symmetries can be mathematically described by June foldable which is similar to the Heisenberg double describing a faith based, but they are different in their per song structure.
Qiaoyin Pan: So, looking at this new.
Qiaoyin Pan: This new first custom strengths, we can find a geometrical interpretation of it which, which is discrete hyperbolic geometry.
Qiaoyin Pan: That means that the building blocks of the discrete juncture are curved not only at the dynamic level but also at UCLA medical level, so we can see it, we can.
Qiaoyin Pan: We find that the castle strange when we are considering travel and graph or for triangulation of the surface, the east coast, the hyperbolic sign lot of a hyperbolic triangle.
Qiaoyin Pan: And the fact that constraints it encodes that it's Derby sense that I ITO angle between the hyperbolic triangle, when we do these triangle together to form a 3D geometry so.
Qiaoyin Pan: So far, actually we we've got and it's part of what we want it switches to describe curriculum to with curfew building blocks, and this is really because we have chosen.
Qiaoyin Pan: A certain decomposition of the face face variable so that gives us a new notion of the symmetry, which includes the curve geometry and and what's.
Qiaoyin Pan: important is that because we have the Carson street that correspond to have pollock geometry our building blocks from the Pack in a medical a box, though, is also correct.
Qiaoyin Pan: Let me give some remarks on this deform look up the face face the first.
Qiaoyin Pan: The first one is that the form fluxus actually have a whole animal nature, in a sense that they act as a parallel transport, it can be seen from this room and graph because here the fluxus and hollowness are both assigned to the side of the ribbon so they are kind of in the same footing.
Qiaoyin Pan: This is not the case in the case, in fact, because we, the process is is viewed as a vector.
Qiaoyin Pan: And more important remark here is that this default a space can actually be derived from the continuous theory, and this is given by this reason work, the key idea of this situation is that we can perform a canonical transformation.
Qiaoyin Pan: Which is induced by a boundary term, which is a function of the frame food and natural constant and the result of this canonical transformation is that we work on an a frame which is value in into the algebra and new connection value in Su to connection.
Qiaoyin Pan: To the algebra and by this change the symmetry the note of signatures also it's also changed by it's changed from a page transformation that is independent of rhonda.
Qiaoyin Pan: A translation, depending on the Lambda to both of them dependent of Lambda so upon some properties to decision process, we can get.
Qiaoyin Pan: Our the form face face described by into flux and, as you two homies and the symmetry is also promoted to a discrete notion, so you can do this.
Qiaoyin Pan: A canonical transformation by the change of symmetries that we are building instead of building the curve launch you with the flat pieces back to the business, we are really building the curmudgeon with a purpose to the pieces.
Qiaoyin Pan: So that is the look party face face described by them homies and plexus, we can also construct this face face with the form notion of spin us.
Qiaoyin Pan: First, let me mostly but, again, why do you want to work on spinners even in fact case would spin us, we can work with a canonical variables, with a very simple pause on structure.
Qiaoyin Pan: And spin us are also a good tool to construct the coherence being network state and the communist China, which are already very well developed in LPG and simple model by many words in this incomplete list of orders.
Qiaoyin Pan: And they can be used to describe the symmetry of the wellness space, also the spinners can be used to construct or the Su to marry up so both in a highest being rotations as they live in the spring, one half.
Qiaoyin Pan: And the question is, why do we want a deformed or some spinners wind alumnus non zero I can we just use this spinners to construct them.
Qiaoyin Pan: that the reason is that first we tend to construct and you que Su to embarrass absorbers in the quantum level.
Qiaoyin Pan: And it's it's also it's suggested in Harlem model, for example, people more and also who we want to build a curve is quick geometries which cannot be done if we just use this business.
Qiaoyin Pan: So how do we how what how What do we want to get from these different spin us we have.
Qiaoyin Pan: We first want to reconstruct the salami influxes so they are consistent and we can we want to reconstruct also all the posts on brackets.
Qiaoyin Pan: We also hope that they are Su to covariance which is stars then it's similar to the spinners we use in fact case, we also want to assign them in a ribbon so we want them to be rated by para transport.
Qiaoyin Pan: And a building blocks to build these defaults Venus I will be caught a couple the font spinner variables and here's a couple of in coast, the cosmos are constant.
Qiaoyin Pan: And they are defined with spinner times a function of this cutter and unknown and a normal of the spinners and they are with.
Qiaoyin Pan: The phone notion before version of the song for some brackets, I want to use these to construct for the form spin us, because we want to assign them to the four corners of written.
Qiaoyin Pan: So.
Qiaoyin Pan: As I said, we want them to be Su to covariance, but when we solve the equations to define the Su to course Venus we can fight only two solutions, what about the rest to.
Qiaoyin Pan: The way we do it is to use the homie nature of the fluxes, that is, we can pair of transport these Su to covariance Venus and construction.
Qiaoyin Pan: Another version of the default spinner, which is what we call here the Brady covariance penis in a sense that, under the Su to transformation, the result is get the result is parameters by another Su to another Su to.
Qiaoyin Pan: parameter but it's related to the original one by the by the by the end to action of the fluxus.
Qiaoyin Pan: So we can from these equations, we can also find two solutions.
Qiaoyin Pan: The results that we get for spinners for the form spinners two of them are as usual current spinners and the other two are brightly colored spinners.
Qiaoyin Pan: And they are related by either Su true or am to pair of transport, so we can assign them to the corner cultural economy of a ribbon.
Qiaoyin Pan: Also, as expected, they can be used to reconstruct all the armies and fluxus and all their posts on structures, so we really get a very nice structure with this default spinners and it's and it's really a information from the fat picture.
Qiaoyin Pan: The reason we wanted to find this default spinners is because we want to construct a phobos with them.
Qiaoyin Pan: First example of the October, those are the scale of product of these different spinners and.
Qiaoyin Pan: In a non trivial non trivial scale across other scale of product of spinners from different links so in the ribbon picture were constructed, we can construct.
Qiaoyin Pan: The default spinners from different ribbons and the spinners we can choose are those that meet at the same corner, but they are from different links so here T ones from Ligue one in.
Qiaoyin Pan: This town to it's from the link to and, indeed, because what four different the ponds been assigned to the four corners when we when we change the orientation of any of the links.
Qiaoyin Pan: We need to choose a different different different business, so we have different expression for this scale of products.
Qiaoyin Pan: it's not straightforward, but you can be checked up or this expression pause on camille's with the with the Su to transformation generators, so they are all Su to embarrassment absorbs.
Qiaoyin Pan: So these are the storm look where are the faith based described by the homeless and the form beforehand before spinners let's see.
Qiaoyin Pan: How we can contact them and see what is the result, or do we get after the organization, we first work on the hollowness and fluxus.
Qiaoyin Pan: By the standard conversations schemes we includes two steps The first one is to quantify the process and how armies into operators which we record them the quantum quantum.
Qiaoyin Pan: quantum plexus the second step, the second step is to conquer the classical or matrix into.
Qiaoyin Pan: quantum our matrix, which is a which can be which can recover this classical arm witches at when we expand this quantum our majors.
Qiaoyin Pan: And this class kilometers squared recover and the first order of the H bar when we arrived this our matrix.
Qiaoyin Pan: into a fundamental realization is expressed as a four by four matrix and the matrix elements is parameters by Q parameter, which in coasts.
Qiaoyin Pan: and London in this cuppa cuppa parameter and it's also in coast, the HR information so one can immediately realize that these are matrix is just the quantum our managers of the quantum group UK us when we write that into in represent you know from from a mental substation.
Qiaoyin Pan: So we do so, we can now see that we get a good structure after we contact them and.
Qiaoyin Pan: What I want to emphasize here is that we get the quantum restructure our natural sort of we just put a hand in his colonized we in in a in quantity in quantization in particular.
Qiaoyin Pan: in a particular way, but this quantum structure is really sourced from the person structure in the classical level.
Qiaoyin Pan: which can be seen, after these two steps we can contact the person structure or some brackets written with the classical our paychecks into communication relations of this quantum Hello armies and quantum boxes in terms of the quantum our matrix.
Qiaoyin Pan: And this competition relations are just defining defining defining relations have some particular groups and what are these particular groups, it turns out that the quantum fluxus.
Qiaoyin Pan: Are in UK English as soon true or.
Qiaoyin Pan: You que Su true and the quantum Hello enemies are in as UK English to Su q2 respectively, so what we see after week after week, one is it is we get a both a Q and Q inverse affirmation of the classical groups.
Qiaoyin Pan: Although I am not giving more details about these quantum quantum group structure and we'll just.
Qiaoyin Pan: Let me just say that we can find the exact expression for this column foxes from a community relations and the definition of the quantum group you que Su to, and you can use as to true.
Qiaoyin Pan: And this exact expression is in terms of the generators of the eucharist future and you could invest into which actually identified.
Qiaoyin Pan: With this exact expression of the complexes we can construct the quantum thousand constraints.
Qiaoyin Pan: With the Co product of this quantum quantum fluxus because they should act on the different particle space.
Qiaoyin Pan: With and we can also solve to get up to in Atlanta with this quantum thousand strengths and this this in Aquinas would be on criteria when we can start a quantum observable.
Qiaoyin Pan: and
Qiaoyin Pan: An interested, we can get from this construction is that we can give a geometrical interpretation to this quantum our matrix can interbreed as some sort of.
Qiaoyin Pan: quantum quantum is, in the sense that eating codes, the condom romy and quantum process is tools in it to space is to subspace It can be seen from looking at it.
Qiaoyin Pan: Looking at the quantum jump back seat cushion that this army just was satisfied by definition we can choose some particular.
Qiaoyin Pan: representation for these two subspace and this.
Qiaoyin Pan: Now Max equation you're calling a mixtape creation can be written in two different ways, one way is just the same way suck the same combination relations as the quantum Columbus and the other way is to.
Qiaoyin Pan: In the same way as the competition relations of the quantum success, but this reformulation are not new in mathematics, but here, these majors quarter majors altitude and.
Qiaoyin Pan: And you to hear or read a quantum quantum palomas and encode them pair of transport, and it goes the notional para transport.
Qiaoyin Pan: When people use the images and then usually codes them right some breathing because of some non committal activity.
Qiaoyin Pan: And here in our picture this braiding is just a pair of transport if we you if we see it in the in our ribbon picture, so we hope that this new way to see the quantum quantum army just can bring some new angle that we use the common groups, including route.
Qiaoyin Pan: So, now that we have that we can't we have kwanchai.
Qiaoyin Pan: fluxus and how long is it also contains the form spinners we just defining the classical level, the key thing is to find a colonization map.
Qiaoyin Pan: And, in fact, if you already get most of the ingredients of it, because we have the relation between the fluxus in terms of the couple of the fonts being a variables, we also have constructed.
Qiaoyin Pan: The quantization of this fluxus into the quantum plexus which is written in terms of the eucharist to generators.
Qiaoyin Pan: And in in and remaining ingredient is the daughter map a map these generators into a queue commodity oscillators which are based these.
Qiaoyin Pan: Before motion of the community relations, so this gives up the conversation map of the copper deformed spinner variables and it turns out that this colonization map is quite simple so just quantifies this kabaddi forms because into the holographic.
Qiaoyin Pan: The holographic cover difference between variables into the emulation operators and quantifies their contract, a more complex conjugate into the creation operators, so this connotation map just are consistent with the quantization map of the corner of the fluxus and Hello miss in an.
Qiaoyin Pan: In an exact expression.
Qiaoyin Pan: So with this conversation map, we can just quantifies the default spinner which is defined with those cup of tea form spinner variables, so we can do, form the form, all these different spinners the four different spin, the question is.
Qiaoyin Pan: In what sense in full quantify some of the most sense can we call them call them spinners because call them spinners, by definition, they should satisfy these two.
Qiaoyin Pan: Relations The first one is that under certain generators anonymous generators of certain quantum groups and what certain action they should behave in this certain way.
Qiaoyin Pan: And secondly, they should satisfy the witness card theorem so with these two criteria we can checked that this the Su to covariance business, they are contest to us to to consciousness.
Qiaoyin Pan: And this break covariance business their contracts to UK inverse Su two columns minutes, so we again see that Q and Q in was defamation when we can't stop it from spinners just as.
Qiaoyin Pan: Just as we saw in the connotation of the factors and how long is and this action to define them to be a up are you queen was a Su to quantum spinners are the joint action of YouTube as you true or you can email us as YouTube.
Qiaoyin Pan: what's also Nice is that they can also, we can also use this quantum spinners to define to reconstruct the quantum pelamis, and this is just in the similar way as it as it classical classical counterpart, so we, we can have this is the ribbon picture of the classical spinners.
Qiaoyin Pan: And the classical Hello miss and process, we can just have a natural quantum picture of this and, for example here the salami quantum maloney's.
Qiaoyin Pan: You can be reconstructed, with the difference in a just attached to teach this to end and can be checked that it's it's valued in Su P equals two.
Qiaoyin Pan: And not just not only the quantum spin quantum armies and quantum process can be reconstructed or their relations or their competition relations can be reconstructed what's the single competition relations of the Q hematoma Q Hammadi oscillators.
Qiaoyin Pan: And with these just what we just define the quantum spinners okay use them to construct the quantum absorb.
Qiaoyin Pan: That is the first one, we can construct is the condensation of the scale of product into a special operators what we what we what they are, they are defined with the quantum spinners.
Qiaoyin Pan: are just attached to the corner, that the two ribbons meet, for example, it's used for here, I hear it gives the orientation of the links.
Qiaoyin Pan: He want to eat too, and we just use the corresponding spinner the corresponding column spin us to construct the skill operators and we can checked by its action on the final result from the gout quantum gas constraints that they are you can do to interrupt so books.
Qiaoyin Pan: So these are the chemical structure.
Qiaoyin Pan: You can also construct the dynamical structure and in this part I will specialize in constructing the hamiltonian in in the spinner substations So what we want to do is to express this new hamiltonian constraint, or the Franklin street with the spinners.
Qiaoyin Pan: To do that, we can we can construct the scale of products have to spinners that is seats on the on the boundary of a loop, for example, however, once penis on link one.
Qiaoyin Pan: And the other spin on the link P, so we can use two ways to pair of transport is the spinner on link one either around the counter clockwise direction or long that clockwise direction.
Qiaoyin Pan: Then the next we can express all these Hello enemies in terms of spinners which gives us the hamiltonian constraints written only with the scale of products of the.
Qiaoyin Pan: Before spinners with since we have the scale of products, we are quantcast this case scale of products into scale operators which defines us a quantum default hamiltonian.
Qiaoyin Pan: With this, we can solve these hamiltonian and what we find is that, firstly, this content hematoma constraint generates that recurrence relate recursion relations of the Q 60 symbol, you can be seen if we consider the triangle triangle face or, in particular the tetrahedron graph.
Qiaoyin Pan: On the other hand, we can we can find that the fiscal states where we solve for different brands, but related by the packet of moose they are proportional to the Q SR a symbol.
Qiaoyin Pan: These two property can give us a link between the qt from equity reconstruct here to the to review and modal, in particular, we can see it in vertical on the clues or.
Qiaoyin Pan: cues extra symbol or actually the vertex and a tooth of the River river model and this ricochet relations of the key to success in both.
Qiaoyin Pan: The in coast, the symmetry of the to be model, so this link is just a default version of the link between the equity and the original which is described in detail in this works.
Qiaoyin Pan: So let me summarize.
Qiaoyin Pan: We can now answer the question within our default rpg model, the question I posted it in the title, so how the cost model constant cutie forms the sandwiches in El que je.
Qiaoyin Pan: be finding this model that yaki geez deformed both at the kingdom medical and dynamic level and also both at the classical and quantum levels.
Qiaoyin Pan: So, as some examples, the momentum spaces thought the form from the are three 2am to group and spinners out the form the hematoma is also the form and this defamation ocean, they are promoted to the key information when we when we can't hide them.
Qiaoyin Pan: So this is good information on the property of the appearance.
Qiaoyin Pan: This cute defamation and restart of the appearance of common groups so.
Qiaoyin Pan: One main point is that this current group to appear natural unicorn theory, in the sense that, so this core group.
Qiaoyin Pan: We searched for the source of it it's because, even in the continuous theory we work on change of variables, so it gives us a new canonical variables, which is the new notion of cemeteries after a proper Disputation we work on a new variables in a blue practice space which.
Qiaoyin Pan: which includes the new discrete national of symmetry and this district notion of symmetry and encode the curved geometry in the kinematics and dynamical level, and these are.
Qiaoyin Pan: These these leads to the canonical structure, when we call entice them, so we see that interplay between the curve geometry and quantum structure.
Qiaoyin Pan: So.
Qiaoyin Pan: Also you've seen from the quantum cuny for hamiltonian the link between the cuneiform equity model we've been here and the connection and it's connection with the people model.
Qiaoyin Pan: In the Indeed we restricted ourself here, in the case of you, creating a signature and negative because moto constant, we can also work on other cases.
Qiaoyin Pan: For example, that you clean his nature of the positive cause muscle constant and, in this case the key was taken to be the rural community.
Qiaoyin Pan: And we need to do with them, we need to do with the construction of the class I have algebra.
Qiaoyin Pan: And we also work on the Ukrainians feature there, in which case when it's a positive customer to a constant.
Qiaoyin Pan: The free space is so to see which also admits a he was already composition, also in the negative cosmetic on constant case it's the first base can also.
Qiaoyin Pan: admit I us about the position, so they should also give us the heisman description of this space as another application, since we define.
Qiaoyin Pan: The phone spinners here we we can use this default spinners to construct the qt form coherent states weeks, which are expected to help us to describe the the deformed either time or space.
Qiaoyin Pan: And then the interesting question, we can ask is how does this model help us to understand 40 from gravity, so we.
Qiaoyin Pan: We see that there's there may be some ideas we can bring to the 40 The first one is that we can be with the curve geometry really with the Caribbean blocks and is in our model we've seen as an example of this application we've seen that you can describe.
Qiaoyin Pan: The struck the faith based a structure in classical and it's conversation in a mathematical well defined way and it gives us a reform it gives us a different version of many notion in a fat case and we it gives us a.
Qiaoyin Pan: nice way to treat the symmetry and describe the cemeteries.
Qiaoyin Pan: And I idea we can bring a Stat here we it's based on it's based on working with on a new variables so by.
Qiaoyin Pan: With the canonical transmission, then we can actually we with whether we can use some similar canonical transformation for the then gives us.
Qiaoyin Pan: Our new canonical variables, which leads to the forms me cheese, of course, we hope that this Defense mature would be related to the current building blocks.
Qiaoyin Pan: And this direction has been initiated in this reason work so The hope is that this approach when we explored it to 40, we hope that you can give us a reliable answer to this long lasting question is that women could structure in fourth dimension.
Qiaoyin Pan: In the gravity.
Qiaoyin Pan: Thank you.
Jorge Pullin: See questions I see.
Jorge Pullin: unraced.
Western LQG Group: hi I have two questions.
Jorge Pullin: I think she's your answer.
Western LQG Group: i'm okay i'm not, what can you hear me, can you just get a kind of get a yes, this is catalog in London.
Western LQG Group: Okay i'm, in fact, I have three questions, maybe the dog a short um first one, just to understand you you.
Western LQG Group: You touch them.
Western LQG Group: Religion to try zero at the end.
Western LQG Group: which was what.
Western LQG Group: What was.
Western LQG Group: kind of questioning I.
Western LQG Group: I was here a while you were talking.
Western LQG Group: So the question is, for the first question for is.
Western LQG Group: very impressive this construction in very, very beautiful very nice and probably very sort of vaguely you beautiful than 40 now.
Western LQG Group: In 3D should, I think.
Western LQG Group: From the perspective of physics, as a way in 3D as of opening up.
Western LQG Group: The viewer theory.
Western LQG Group: And sort of seeing structures in it.
Western LQG Group: Or should I see it.
Western LQG Group: As a different theory at different quantum theory of geometry 3D its first question.
Qiaoyin Pan: Sorry, to call us said again use the term know as a different model.
Western LQG Group: yeah the relation between this theory you're describing into a zero.
Western LQG Group: Is the same.
Western LQG Group: For for the physical perspective is the same theory of quantum.
Western LQG Group: geometry.
Western LQG Group: Or is a different one so you're sort of opening up to.
Western LQG Group: Zero and showing ways to what is inside the mathematics inside or you're defining a different theory.
Qiaoyin Pan: I would say that it's the same theory, because we can in with your remote, so the vertex and it is given by a ques extreme with.
Qiaoyin Pan: it's been shown that this Q 16 a symbol represent a curve triangle, which is the result from including the cosmological constant to curve, the usual tetrahedral interrupted region so here also we are using this curve geometry so from this In this sense, they are describing the same geometry.
Western LQG Group: Okay second question it's a just.
Western LQG Group: like clarification on maybe.
Western LQG Group: It seems to me correct me federal this the quantum spinner you introduce.
Our.
Western LQG Group: Different variables.
Western LQG Group: For describing.
Western LQG Group: The geometry right so they're not physical spindles they are, they are.
Western LQG Group: they're not electrons are.
Western LQG Group: On top of the of the gravitational field.
Western LQG Group: If you have not the correct me if i'm wrong now, could the same.
Western LQG Group: notion of spinners to.
Western LQG Group: Somehow could be saying that semantics, be used to instead to.
Qiaoyin Pan: Actually couples spinners to the.
agility.
Qiaoyin Pan: Physical speedos electrons.
Western LQG Group: newlands ports.
Qiaoyin Pan: For the latter part i'm not sure if we can, coupled with the physical particle but um this is um well enough for them, since they are the they are the quantum submitted that can be used to define a Q vectors in any higher speeds.
Qiaoyin Pan: So it's not that we just define an new notion spinners but they they are, they are not used to describe vectors that can be used to describe.
Qiaoyin Pan: Practice but cuneiform vectors, which is a well we use them cuneiform the cube catch colon coefficients to a couple to the quantum spinners which will give us the cues vectors.
Western LQG Group: and
Qiaoyin Pan: Life Sciences answer a question.
Western LQG Group: Not a sort of 70s stood.
Western LQG Group: Maybe I misunderstood.
Western LQG Group: The question is that there's been a few.
Western LQG Group: Introduce are not new degrees of freedom right that the same degrees of freedom that you're flexing salamis.
Western LQG Group: they're just different variables describe those degrees of freedom.
Western LQG Group: Exactly is that.
Western LQG Group: safari i'm a writer oh.
Qiaoyin Pan: Oh well, the frat spinners they did not include the customer to constant, but the difference Tina they are written with them, so we can see it's a function of the customer constant.
Western LQG Group: Now that's because.
Florian Girelli: If I may interject, you are right now for.
Florian Girelli: The nose address for gravity, so they are reading books to read fractures default or not actually have you know, three or four must be knows.
Florian Girelli: But they are just to their to their order via version to find the discrete join me.
Florian Girelli: it's a no brainer i'm not i'm not aware of ways to connect this you know to matter spinners.
Florian Girelli: Gone will know, but I love to.
shop.
Western LQG Group: Okay wonderful.
Western LQG Group: Wonderful wonderful, thank you, thank you, thank you, sorry, it was not understanding that that's clarify and the last question, if I still if i'm not taking too much time, this is a.
Western LQG Group: This is a very general question so if you don't know the answer to the answer I don't get the answer i'm used to get so but but I try.
Western LQG Group: In the mathematics of the information that i'm there is not after the beautiful there's no action of Su to directly of these variables so.
Western LQG Group: physically.
Western LQG Group: The opposite direction is different for the X.
And the y directions.
Western LQG Group: And they also usually get the yeah but it's not easy to environment, this is cuda for.
Western LQG Group: Funding but does this mean that.
Western LQG Group: In a theory like this, based on this mathematics.
Western LQG Group: At the end of the day, the physical.
Western LQG Group: directions of.
Western LQG Group: Any three dimensional space and not.
Western LQG Group: The same as sort of distinguishable but by mean of.
Western LQG Group: quantum more.
Western LQG Group: experiment that involved because we're logical.
Western LQG Group: constants or not.
Western LQG Group: And if not, why there.
Western LQG Group: isn't an actual issue to.
Western LQG Group: So three.
Western LQG Group: Acting and somehow.
What.
Qiaoyin Pan: You mean what, why is there, so three in a fat case.
Western LQG Group: I mean in physics in the physical space, the three directions at the same way, this is is a is an obvious rotational invariance in the.
Western LQG Group: In the.
Western LQG Group: And no indication that is broken.
Western LQG Group: But did the math of Su Tu que.
Western LQG Group: It is broken oh my role.
Qiaoyin Pan: i'm honestly it's broken.
Qiaoyin Pan: i'll say so defamation, we can recover the esteem to when we take the fat limits also maybe, so it seems that the answer questions well.
Western LQG Group: We can recover, but the in some limit.
Western LQG Group: But yes reality is not.
Qiaoyin Pan: For defamation.
Western LQG Group: So, in a in an actual theory if if the real world is described at this, but the.
metrics.
Western LQG Group: and
Not in some limits.
Western LQG Group: It if i'm here isn't one direction different than the others, which is the.
The Tuesday directions.
Qiaoyin Pan: hmm.
Qiaoyin Pan: I don't think, so I think when we describe this the formed que es deformed cuneiform killed information, yes, we do to say that the Russian a prison with defining the end to group.
Qiaoyin Pan: By month we choose merchants, so that we can define that in what in a proper way, but we can also choose another direction, which is just a rotations of this special direction and still defining he as morphic group.
Western LQG Group: So you think at the end of the day, your service would not distinguish.
Western LQG Group: direction.
Qiaoyin Pan: I think so.
Western LQG Group: Okay okay yeah that's i'm happy that you answered this, this is what a.
Western LQG Group: Somehow i've never been able to see a.
Western LQG Group: Clear argument here, but maybe this is a very general question about the use of what two groups which I sort of bothering me all the time if anybody has an answer i'm happy to.
Marc Geiller: Also, Carlo, if I may, these are internal directions right so should it matter at all, or because.
Marc Geiller: I mean it's a.
Western LQG Group: it's a very good point, but how do I from here, go to see that the known internal directions, is an so three acting on demand end of the day.
Muxin Han: So there's there's arguments and reach from different perspective, so you can think about.
Muxin Han: kirkpatrick here tetrahedron versus the flatter quicker and I email king and this this quantum growth tracker is completely it is consistent with the rotation symmetry is now there's no interest is inconsistency.
Muxin Han: So three rotation and the resolution is, is that you can see, there are curved tetrahedron instead of a flat equity curve tetrahedron locally.
Muxin Han: To protect you have just perfectly so three rotations but the difference between curb tetrahedron and flat type of even said, you have pelo transport if you it's not like you have at the Center also.
Muxin Han: yeah you help the closure the linear closure like flat in Cleveland and and you have to Palo transport your your vectors from the vertex and to.
Muxin Han: somewhere else, and these because it's curved type of food and you have non trivial pellet transportation yeah and these non non trivial pelo transportation actually is the surgeon, the reason for for for this Su Tu que defamation.
Western LQG Group: yeah so you're saying I get it so you're saying once I I can do to the gentleman to the the preferred cuter can disappears I just see the, the only thing I see is this local convergence of the say.
Muxin Han: Yes, yeah yes, so these two is certain reflection of of these these curvature this cosmic converter inside yeah although is not is.
Muxin Han: Now I will say it turns out it's it's the connection is, you have to dig out the Firstly, you have to study the closure and then quanta disclosure and then you can see, they can see that the quantum group, as you to Q emerge from that.
Western LQG Group: OK OK OK.
Deepak Vaid: OK yeah.
Muxin Han: On classical classical.
Muxin Han: classical counterpart of this so Tokyo is a curve typically that's that's the point okay.
Deepak Vaid: Thank you, is it Okay, if I jump in and just try to answer, maybe Carlos two points.
Deepak Vaid: All right, thanks so Carlo one, the first statement that you made was.
Deepak Vaid: These these spinner variables right yeah.
Deepak Vaid: Why why can't we think of them as like or why can't we use this technology to couple matter to gravity right.
Deepak Vaid: yeah now another another perspective that one can take is that you know why not interpret the spinners themselves as representing matter degrees of freedom.
Deepak Vaid: I mean after all those in that whatever.
Western LQG Group: Well there's an equation that connects to the normal reflex variables, so they are not dependent.
Deepak Vaid: know that that's that's right, but the I mean it's like if it walks like a duck and talks like a duck.
Is that a dark right.
Western LQG Group: yeah.
So.
Deepak Vaid: that's my that's my perspective, and the second thing is that see an automated if this somebody might make it back no will work wanting to gravity, there is no matter here right we didn't put any mattering.
Deepak Vaid: Yes, Rachel then again the argument my My response to that would be that will be that it doesn't really make sense to quantify your crappy.
Deepak Vaid: Right, I mean I mean you might think that so, so there are many arguments for why there is a reason, we should not expect there to exist, a theory of quantum gravity without matter.
Western LQG Group: Right I don't mind a little I don't buy those out with any of them.
Deepak Vaid: No, no that's that's fine many people don't buy that argument that's fine but.
Deepak Vaid: Anyway, that's that's what I wanted to.
Western LQG Group: know I see I see what you say so so let's take this really seriously and say okay here's some speedos that's what you say right so but.
Western LQG Group: But these are not the electrons.
Western LQG Group: These are not the electrons you, you would agree with that these are not this not works.
Deepak Vaid: No, there is a reprimand you.
Deepak Vaid: know that right because, for one thing.
Deepak Vaid: You know the winners represent non momentum so if you think of them as part of the APP to be masters particle.
Western LQG Group: Okay.
Deepak Vaid: But, but then there is no reason to not think of them as master particle.
Deepak Vaid: and
Western LQG Group: Then he says he shows names okay fine, but then, this is still a gravitational field was just describing this Venus is more similar to matter but it's still something else.
Deepak Vaid: Well, I mean I don't want to fight right too far from the topic of the of the.
Deepak Vaid: Of the.
Western LQG Group: Okay okay.
Western LQG Group: I get it, but I got you for Thank you yeah.
Hal Haggard: also had a comment.
Hal Haggard: Go ahead.
Wolfgang Wieland: Maybe one should also point out to make the difference to the spinner variables in 4d the these really transform under under matrix representation of depending on the cosmological constant as a to see or.
Wolfgang Wieland: As you as you want one or whatever, depending on the sign of the cosmological constant so, in other words, they are speedos for the for the deceitful for not for the for.
Wolfgang Wieland: A bit different than then spinners for the spin connection, which is.
Wolfgang Wieland: Maybe a bit confusing, but they are in that sense, then those are not, if you would cover an electron in two plus one you wouldn't use is.
Western LQG Group: Very good.
Wolfgang Wieland: So I will.
Wolfgang Wieland: say that that really geometrically describe geometry not.
Western LQG Group: Better.
Western LQG Group: That kills Venus.
Wolfgang Wieland: is really cool stuff.
Jorge Pullin: Oh i'll.
Hal Haggard: add just a quick comment on your last question.
Hal Haggard: Carlo because.
Hal Haggard: That question has long puzzled me this question of the breaking the fact that cue to form seems to break the symmetry and what's going on.
Hal Haggard: And I have a toy model, where I can work things out, and I can kind of see how it works, so if you study, not a harmonic oscillator in a plane, but a harmonic oscillator on the sphere.
Hal Haggard: So it's a central potential on the sphere, and you think of the tangent plane to the sphere say at the North Pole.
Hal Haggard: You can project, the orbits from the sphere via gnomic projection via projection from the Center on to that tangent plane.
Hal Haggard: And it turns out, you map orbits of the harmonic oscillator onto orbits of the harmonic oscillator in a non trivial fashion.
Hal Haggard: And you get a cue to formed harmonic oscillator on the plane and it's a really beautiful way to see how cute affirmation comes about.
Hal Haggard: Now, if the underlying space is the spiritual space it's clear, you have an s3 rotation, but having chosen one tangent plane to project the motion on to breaks that it chooses say the Z axis as special.
Hal Haggard: And so, your symmetry has a certain image on the plane that looks to have a broken cemetery.
Hal Haggard: But it's not really a broken symmetry of the of the overall system, but just the view representation that you're looking at it under.
Hal Haggard: So this is kind of a toy model for understanding that that there's kind of two things happening there's the underlying system and its physical symmetry and then there's a choice of how I view that system.
Hal Haggard: And that choice of how I view it can break the way the symmetry appears in that representation.
Western LQG Group: Well that's fantastic that's that's great that's clarified, you have just written.
Hal Haggard: I i've been working on it for long and I don't know another year.
Western LQG Group: OK OK, I think I get the point, thank you, thank you very.
Qiaoyin Pan: Much Thank you.
Deepak Vaid: For coming this point, if I may just add to what health and please correct me if my reasoning is incorrect.
Deepak Vaid: That.
Deepak Vaid: Even when we work with the ordinary quantum theory of angular momentum right, we have the generators and we make a choice of which is the data.
Deepak Vaid: Right, so we have n squared and there are there right so when you want to talk about the states have a proper spelling particle right, we have to talk about, we have to pick a certain action so but that doesn't mean.
Deepak Vaid: That you know the rotation of symmetry of the system is broken right.
Western LQG Group: So you're saying it's the same is the same thing, yes okay miss.
Deepak Vaid: It seems to me that and also there are there's another anyway yeah that's it for now too many points I don't want to make.
Western LQG Group: Okay, thank you.
Hal Haggard: So deepak I don't really disagree with anything you said but I always felt like that was too weak a statement just to say yeah we make a choice of one of the generators and then it's special.
Hal Haggard: It for me it kind of loses the geometrical interpretation of the thing as a symmetry and that's why I wanted to find a model where I could see that more deeply.
Deepak Vaid: know the picture that you described is really is really elegant and so, if if your idea is it.
Deepak Vaid: I mean.
Hal Haggard: It has a long history, so, in fact, in a sense, Q defamation could have been discovered much earlier.
Hal Haggard: The the wonderful.
Hal Haggard: higgs of the higgs boson was the first one to notice that you could study the harmonic oscillator on the sphere and to end to find the symmetry algebra.
Hal Haggard: And it's very interesting very subtle it somehow a truncation of the cuda formed algebra it's not the full Q deformed algebra it's truncated instead of having to go to every order in the generators you, you only have to go up to a finite number of orders in the generators.
Hal Haggard: And and that's partly how higgs got there but, but so No, this is an old idea that i'm trying to elaborate in a way that makes clarifies cute information.
Deepak Vaid: I, there is another reason for why one would expect that if you were talking about clue defamation, there would be a preferred direction.
Deepak Vaid: And again, Charlie and I forgive me if I say your name incorrectly but.
Deepak Vaid: It was like okay Thank you so.
Deepak Vaid: So you correct me if I if i'm mistaken that when you talk about Su defamation right what you're doing is you're you're you're geometry becomes non complicated right so when you when you describe.
Deepak Vaid: You know, a field fury want some space and you say that well it.
Deepak Vaid: transforms under Su Tu que.
Deepak Vaid: So the interpretation of that is that the underlying facetime becomes more complicated and the way that physically that one can think of it.
Deepak Vaid: is to imagine that there is a magnetic field.
Deepak Vaid: Right, so when you have a magnetic field, what happens is.
Deepak Vaid: And you know you're talking about some particles moving in in a plane.
Deepak Vaid: And you build up the pace pace of those particles right, then you find that the momentum variable or non competitive because of the presence of the magnetic.
Deepak Vaid: Right so.
Deepak Vaid: The be you know um.
Deepak Vaid: I don't know off the top of my head the exact steps, one would take to go from one to the other, but it seems to me that that you know it's.
Deepak Vaid: analogous situation.
Qiaoyin Pan: So we're seeing that you use this Su q2 to para transport it.
Qiaoyin Pan: So I think I didn't really get the point.
Deepak Vaid: No i'm talking about non quantitative.
Qiaoyin Pan: geometry right.
Deepak Vaid: So non quantitative geometry points to the shows up in the point of all of that.
Deepak Vaid: Right, so when it when you're trying to.
Deepak Vaid: So, as you to Q is related to non competitive geometry right.
Deepak Vaid: If you read, so what happens in the simplest model of non competitive geometry.
Deepak Vaid: Which is in the quantum all effect right, you have a particle moving in a plane and there's a magnetic field transfers to the same.
Deepak Vaid: And due to the presence of the magnetic fee.
Deepak Vaid: Being the momentum generators of the particle the X, Y generators they become.
Deepak Vaid: They are they are changed because of presence of gauge field, and when you calculate the accommodator is no longer valid.
Deepak Vaid: Otherwise, if you have a particle you know you would expect this momentum momentum components to commune.
Deepak Vaid: So so so that is the simplest physical model that I know of non competitive.
Deepak Vaid: So, so in that you are picking a magnetic field you're.
Deepak Vaid: singling out the direction is.
Deepak Vaid: Not what extent this applies to your picture and I don't know.
Qiaoyin Pan: What should the relational this with the boys on the Hong Kong boy effects huh.
Qiaoyin Pan: yeah so I cannot give a concrete answer to that.
Deepak Vaid: yeah no i'll just go ahead.
Qiaoyin Pan: and give the.
Deepak Vaid: answer here.
Florian Girelli: I think, maybe usually that some type of non committal activity i'm not trying to create the form.
Florian Girelli: One community.
Florian Girelli: I think when you have too many ticket is more activity feed is a constant.
Florian Girelli: rate and it's much more Maria.
Florian Girelli: Maria is not good information.
Deepak Vaid: That they're not like a mapping between that and the Su Tu que or the new default.
Deepak Vaid: Group.
Deepak Vaid: I thought I thought you could go from one to the other that that's where I might be wrong.
Florian Girelli: Nothing, there are different types of one committed to the team or your or cutie formation and one is with a constant term.
Florian Girelli: X X would be a constant time was this one is quality or the automatic automatic not committed to it.
Florian Girelli: i'm not too sure there is a way for you to.
Deepak Vaid: Okay, I might I might be wrong in.
Jorge Pullin: Any more questions.
Jorge Pullin: Okay let's thank.
Qiaoyin Pan: You, thank you for joining, and thanks for the questions and discussion.