Jorge Pullin: So our speaker today is called Zhang will speak about computing expectation rally are called El que je Hamiltonian to next reading order on
Cong Zhang: Okay.
Cong Zhang: So thank you, thank you for the own data so that I can be here to to represent my work. So the title of my work is computing expectation while you have full look quantum gravity Hamiltonian to next to leading holder.
Cong Zhang: And that this is a work in collaboration with Musi hat and the chatroom zone. So here are some song is as is a PhD student of moving hands and in FAQ. So the paper of this work is in preparation.
Cong Zhang: So at the quantum material, it is crucial to ask the H back reaction of loop quantum gravity. So a possible way to see this crowd to see this. The fact that is through the effective haven't Anya, which is motivated by some models in Luke condom cosmology in those models.
Cong Zhang: And effective dynamics and the quantum dynamics are shown to be compatible with each other.
Cong Zhang: And the here that effective dynamics is the dynamics, driven by the effective Hamiltonian and the effective Hamiltonian. You're late is the expectation value of the Hamiltonian operator and Sam a coherent state.
Cong Zhang: So, so we can compute the age back reaction of the expectation value of the Hamiltonian operator to see the H bar correction factor of loop quantum gravity.
Cong Zhang: Some recent work which to get the full loop quantum loop condom gravity having Tanya and is coherent this data.
Cong Zhang: Expectation value as a homogeneous and as a target data to gather effective having Tanya take this foam and
Cong Zhang: With this with this effective Hamiltonian, big data and symmetric bounce. So in my work, we will calculate that this term or each bar.
Cong Zhang: In the full loop quantum gravity framework, however. So the problem here is that the current state is kinematic so we didn't know that much is consistency with the quantum dynamics.
Cong Zhang: Currently there is a new pass integral formulation of loop quantum gravity proposed by Lucy and Hong Kong Leo which release the effective Hamiltonian and the quantum dynamics directly
Cong Zhang: So the idea in this world is to is to is to use the past integral former formula to calculate the effective action.
Cong Zhang: And that they get the following the following equation. So we can see from this equation that the effective action can be related with the
Cong Zhang: Expectation value of the Hamiltonian operator directly. So we will, and also in their work. So they calculate
Cong Zhang: The expectation value of the Hamiltonian operator to the leading order, but in my work. They will, they will compute, not only the leading order, but also the next two leading order in each bar.
Cong Zhang: So what we are doing. More precisely, is as follows. So, so first that can see the a cubic lattice.
Cong Zhang: And then can see there's some coherent state. So, based on this cubic based on this graph.
Cong Zhang: So here, G is some in some in some is some some stuff used to label the coherence data or use that to label the classic office space. And there's an honesty is the dimension lies quantum per meter. So, T is defined here. So, A is a is some parameter of dimension.
Cong Zhang: Of air dimension. So this T is is is is so this is dimension lives and then we will just expand this expectation value with respect to tee up to the next two leading order.
Cong Zhang: So here, this precise this coherent state precise is the is the team and coherent state.
Cong Zhang: So what we are, what we have data is the falling. So we use mathematic mathematical to to to go to some to
Cong Zhang: Some coder and with those with those coder, so we can, for instance, the computer, the expectation value of any minimal operator and also we can we can simplify the operator by by computing the communicator inside that those operators and with those sense of those two functions.
Cong Zhang: Implemented by our coder, so wait calculator, the expectation value of the Hamiltonian operator in the food look quantum gravity framework to get this readout so
Cong Zhang: And what we did is to use some server with two group of 48 core processors and the two parallel computation with 96 kernels for five hours to get this without
Cong Zhang: It should we mentioned that here that although here, we use the homogeneous and so topical coherence data batter our code can be used to an arbitrary keys easily
Cong Zhang: Now light has come to some details about our work. So the first is about. It is our introduction to the team as Coker interstate. So for team as coherent as data. So we have this graph, and that the, this, this, this G is a function from this graph to as out to see. So which satisfy this equation.
Cong Zhang: And the coherence data based on the whole graph is just the inner product. No, no, it's just a tensor product of the as you to coordinate data located at each edge and at each had the coherence data.
Cong Zhang: Looks like this.
Cong Zhang: It should be mentioned here that. So this is our Tuesday element of G can be divided into into this form, and here this an ass and empty are some as you to element.
Cong Zhang: And this see is just a complex number, so we can locate we can distribute that this is an empty to the source ponder and the target ponder of this edge and the located, this, this, this complex numbers. See here.
Cong Zhang: It should be, it should be noticed that. So this as you to element can be related to a unit vector by this by this equation.
Cong Zhang: By this equation. So, this this vector and is is just that the unit vector relating to related to this as you to element, the same for this empty.
Cong Zhang: At the same time, we are each agile, we have three basic operators. So which are the flux operators located at the source ponder of the edge and the target point of the
Cong Zhang: Of this edge and also we have this color Noemi on this edge.
Cong Zhang: It can be proof. It can be proven that. So with respect to the team and coherence data that expectation value of the three basic operators.
Cong Zhang: Satisfied those three equations.
Cong Zhang: And the. Now, let us come to the Hamiltonian constraint and
Simone Speziale: Know about this last statement you made.
Simone Speziale: For all three directions. You can check that expectation values will pick the in the
Simone Speziale: unit normal or just for dessert direction.
Cong Zhang: Full for the three directions, actually. So, so, so I actually didn't understand your question. And that module. So, so, can you can you explain explain a little bit
Simone Speziale: Sure. I mean, by the way, they are constructed. We always got the impression that what they minimize is the uncertainty between
Simone Speziale: The alarm armies and the reflexes not uncertainty. Well, apart from minimizing the uncertainty, but giving precise direction for the flex is not part of the
Simone Speziale: Motivations and what Oliver and Tom I said Shona was that the said component was effectively will pique the with a Gaussian, but I didn't.
Simone Speziale: Never see that they showed it all the components will repeat. And in fact, recently we were investigating how one can modify this proposal, so to have a property like this.
Simone Speziale: More completely implemented so I'm surprised that you're actually saying that it's valid for any direction but
Cong Zhang: Yeah, it's valid for
Cong Zhang: ITV so
Cong Zhang: The barn is W SOS year. I just can't see the abstract add
Cong Zhang: I just can see the upper edge and this after edge.
Cong Zhang: Is is labeled by this date by this date, G, and then we can see that is coherent state. So, we will get this result. So it is enough. So now, so for this readout. There is nothing to do with this cool big lattices actually
Cong Zhang: So you have a coherent state label the by this G. So, and the computer that expectation value of the three operators, you will gather this result and that this an as an empty is from this as our to see element.
Cong Zhang: So it's okay.
Abhay Vasant Ashtekar: So I just wanted to step in and say that may be
Abhay Vasant Ashtekar: Confused confusion is because you are fixing a particular direction space and Simoni wants to, I mean like in the middle of this slide, you say explicitly that there's an equal to and he he
Abhay Vasant Ashtekar: Seems to me that you are fixing a specific direction. Anyway, as opposed to that age. And so the current state is
Abhay Vasant Ashtekar: seems to know not to be no
Cong Zhang: So the on the here, there is nothing to do with the direction of the edge so we that I can give any I can give an arbitrary edge. So like, like a curve. So after add and I just assigned to this edge as our to see element.
Cong Zhang: Okay, so I will get an ass and energy.
Abhay Vasant Ashtekar: That's what I mean. I mean, you're fixing a particular so to see element right
Abhay Vasant Ashtekar: Yes. Oh, yeah.
Abhay Vasant Ashtekar: That that particular asset to say element has some associated with ends in here and
Cong Zhang: And I think. Yes, exactly.
Abhay Vasant Ashtekar: But, but other than I think similar to card that you can do it simultaneously for all
Abhay Vasant Ashtekar: Any empty. Is that what He taught since the morning
Simone Speziale: Yeah, no, but I think what answers my question. Is that I suppose you're thinking the limiting which etc infinity. I mean, the larger areas with right maybe that's what your little Twitter means
Cong Zhang: So you mean this T to infinity.
Cong Zhang: That we didn't either. Yeah, no, we didn't take any limit here.
Simone Speziale: So why do you have these little twiddle there in the equality.
Abhay Vasant Ashtekar: Equality.
Simone Speziale: In the limit of large Geeta, then I understand they agree that's perfectly fine. If it's Valley, the final ito then I surprised, but
Simone Speziale: But this is
Cong Zhang: This is, this is from but this is from
Cong Zhang: Yes, so the partners like you just to do calculation and
Cong Zhang: Oh ok ok ok so here this approximate the equal means. And so they are equal to each other up to the
Cong Zhang: So so so far for the leading order. So, so you can. There is also like a plus some some some some other terms with respect to t like a plus something comes T and the plus something times t square. So, this is this is the this is the meaning
Cong Zhang: Of this so so. OK. OK.
Cong Zhang: OK, so the point like that they are equal to each other in the limit that the T to there.
Simone Speziale: I think you also need large data, but it doesn't matter. I mean, it's an approximation. I might be. Now we glorify the deployment. Thank you.
Cong Zhang: Okay.
Simone Speziale: Okay. Okay. Thank you. Thank you.
Cong Zhang: Okay, so
Cong Zhang: So now, let us go to the Hamiltonian constraint. So, so, for this one, Tony constrained. It is usually divided into
Cong Zhang: Into two part. So why is this Euclidean part and the other is the lorenzen part. So they take this phone and what way data is just a to computer the expectation value of this Euclidean part and also this lorenzen part to get the expectation value up to the next to eating order.
Cong Zhang: Okay, so. So the first problem here is about this volume operator. So, as we know, for this for this definition of the volume operator. It is a square root and under the square root, there is the absolute value and attempting, so this Q operator.
Cong Zhang: So so impressive. But in general, if we want to define if you want to get the readout of this volume operator, we need to first the diagonal lines and this Q operator.
Cong Zhang: Which will be very complicated for us. But as far as the expectation value with respect to the team and coherence data is concerned, so
Cong Zhang: It can be, it was, it was proven in this work by Gisele and the team at in 2007 that this volume operator can be replaced by this by this VTT
Cong Zhang: So, which is just a polynomial of this Q operator and we can so here to see is just as I'm a coefficient
Cong Zhang: Okay, so stop substituted this VTT into the expression of the UK's leading and the lorenzen Hamiltonian, we will get some operator taking this form, so we can see that the adjuster polynomials of flux and anomalies.
Cong Zhang: So now, let us talk about the complexity of the computation. So, so taking the Lawrence, Lawrence lorenzen having Tonya at that example. So, so in this in this expression, they are actually two summations. The first is from the contraction of the indices of anomalies and flexes
Cong Zhang: So, so in this kill, they are those can traction for this for this flax indices. And so here we they calculate the trees and that they are this multiplication of those melanoma, so they are those
Cong Zhang: can adapt those Sam over the polynomial in this is so now if we can see the only the flag, the flag in this is
Cong Zhang: So there will be
Cong Zhang: So bad. Our experience. So there will be at least like 10 to power 10 times of computation. So assume that each time of competition, take a span of one second, we will need a 2000 years to complete this result.
Cong Zhang: And also, if we can see that the the result of the next two leading order. The difference between the result of the leading order and the next to lead in order is the values of those am
Cong Zhang: So if we can see there the next two leading order. So those am is larger than that, if we can see the only the leading order and then we will have 10 two powers 14 times of computation. So, which will which will span the like 2 million years.
Cong Zhang: And also there are this some over there are, there's some over address and the vertices
Cong Zhang: So,
Cong Zhang: According to our according to our competition experience. There are about 10 to five cases for different address and the vertices
Cong Zhang: Which we need to be which we need to consider. So that means when the final computation time to gather final result is is the is this tend to power five multiplied by the time here.
Cong Zhang: And
Cong Zhang: Okay, so, of course, so this is not the reality. This is not the reality. So, otherwise there will be no terrible no be there will not be this, this, this, this presentation.
Cong Zhang: And so, as mentioned about so we compute the with some server and finally take finally only use five hours the pond. Why the reason why the
Cong Zhang: The time use the is so short is is this is this to point at first we found a theory to judge the order of the expectation value.
Cong Zhang: So with this period, we can exclude the cases of in this is for which the expectation values are of hair order and the second is because of our algorithm which which is the standard to avoid repeated computation because of this two point. So our computation complexity decreases exponentially.
Cong Zhang: So the procedure of our competition is the Foley, so at first we simplify the operator to be this form. So the point of this at the point of this of this tab is the foliage so
Cong Zhang: So, so please be reminded that for, for instance, for this lorenzen Hamiltonian operator, there is a or of factor which is of order one over 32 seven
Cong Zhang: So if we didn't. If we didn't, simplify the operator to be this form. So we need to computer that expectation value to order to to power eight so that we can get that expectation value of this operator of this up of the of the Hamiltonian operator to next to leave in order
Cong Zhang: So that that will be very, very complicated.
Cong Zhang: So, so, yeah. And then we just a factor is the operator to expectation values on the individual address and on on each ad is so we just need to
Cong Zhang: We just need to compute the expectation values of mono meals of Holland Ami and Fluxus efficiently, it's, it should be mentioned that hear that. So let f be an operator on this edge and then we can see there is expectation value with respect to some coherence data labeled by G.
Cong Zhang: It can be proved it can be proved that
Cong Zhang: So the expectation value of if with respect to the coconut state label it is equals to the to the expectation value of this app with respect to the coherence data label the by this exponential. Yeah, by this by this is our to say element.
Cong Zhang: So they are equal to each other up to again transformation and this transformation.
Cong Zhang: Depends on this and as an empty. So, because of this to compute the expectation value of this operator with respect to an arbitrary a coherent state, it will be sufficient to consider is expectation value with respect to this to this d
Cong Zhang: So now, now we come to the important the theory them. So the theory them is the following. So let AF be an operator, which is a production of alpha have to, and so on.
Cong Zhang: And assume that there are n zero operators such that their expectation value with respect to the coconut state is of older is an older team. That means the leading order is is this theory of the order of why is there.
Cong Zhang: Then the expectation value of f itself is of older T to power in were an relates to the to the to the to the to the to this to this number and their own. So, here this symbol is the flow of this of this of this of this of this number.
Cong Zhang: Okay, so we can see that the order of this, the order of this, the expectation value of f relate to the number of such operators.
Cong Zhang: So, how to use this, how to use this theory them. It can be used by this one. So now let us assume that if those if I Aflac says all anomalies. So since
Cong Zhang: It can be proof that so this p plus minus y the expectation value of the operator p plus minus one and the expectation value of the melanoma operator.
Cong Zhang: With me that a is not equals to be. So the expectation value of that operators are the zero and the coldness data labeled by z. So, here, here, this p plus and the minus one is defined here.
Cong Zhang: Okay, so, because those operate those the expectation value of those operators are there. So the order of the the order of the expectation value of f is determined by the numbers of such operators p plus and the minus one and also those
Cong Zhang: Are not those who are anonymous with that is a is not equal to be so this period theorem. So we'll finally decrease the competition complexity exponentially.
Cong Zhang: So let her see why. So taking such an operator as an example. So here p is an arbitrary numerical factor. So we have those moments and and the flux is here.
Cong Zhang: Okay. So in general, if we didn't apply the about theory them, we need to consider three to power 3am cases for those in this is alpha, beta and gamma. So, because there is this power am here.
Cong Zhang: So for each alpha, beta and gamma. There are three cases. But if we apply if if they apply the about period them what we will get. So, so, since only the expectation value up to the next to next. The two leading order is is is considered
Cong Zhang: So the about theory them tells us that for those in this is alpha, beta and gamma, so it can only be the three cases. The first kiss is that all in this is our theory. So, we will have only one option. The second case is that. So in those in this is alpha, beta and gamma
Cong Zhang: Their contents, a single plasma or a single manasquan so there will be there will be two times 3am cases.
Cong Zhang: And the third case is that inside those alpha, beta and gamma. There is a pair of plus one minus one or minus one plus four, and then maybe we'll have those options.
Cong Zhang: As far for other case, for instance. There are like two plus one among those alpha, beta and gamma according to the about your rhythm that expectation value will be an older t square. So, they will leave you are not considered a suitcase.
Cong Zhang: So together we will have we will have
Cong Zhang: This times
Cong Zhang: This this terms of options. So we can say comparing them with this three to power 3am it has been decreased exponentially. But we will have more than that.
Cong Zhang: So it can be proof that for the for the for the keys keys to and the history as far as the next, next, the two leading order is considered
Cong Zhang: So, only the relative partition between people, plus and the minus four and also such an enormous matter.
Cong Zhang: So here is an example to to to explain what I mean, so, so, so, so say in the left hand side. So the
Cong Zhang: We have this p plus one and the p zero, but in the right hand side. So the order of this to operator is changed, but the expectation value of this two operators are equal to each other up to the up to the next two leading order.
Cong Zhang: Okay. So, because of this. So, now let us let us review the three cases for the first one. So, there is only one option, but for the father's for the second one. So,
Cong Zhang: Although we have 6am options, but they only need to do two terms of computation. So each is four plus one and each is for the management kids and for the third case, it is the same that we own, we also only need to do two times competition. So together we only need to do five times computation.
Cong Zhang: So compared compared with this, we can see that the terms of competition is decreased exponentially.
Cong Zhang: Okay. Now let us go to the last go to another key point of our of our code. So how to simplify the operator.
Cong Zhang: So, as we mentioned above. So there is this overall factor of that over to to seven in this in this Laurens I'm Tanya so so that we need to simplify our operator. So to computer the communicator. So
Cong Zhang: So let us let us let us see one can be the one competitor like this.
Cong Zhang: So by using the lab me through. So, we will have the readout is the falling. The result is a falling and the to gather to get this result.
Cong Zhang: We need to do an times competition, but because we finally we finally expanded the readout with respect to the older and older so we can compute also this competitor order by order and the result is given by this way. The result is given by this one.
Cong Zhang: So the, the advantage of this of this of this equation is like that. So, now let us at the first ignore the exact value of key just a focus on the, on the, on the last
Cong Zhang: Of the product of the flux operators, so what i mean i mean i mean the falling. So I first define a function in the p
Cong Zhang: So this in the P is a function to to label the least of the flax indices. So, here this one is is used to tell which in the p, it is, and this is the edge where those
Cong Zhang: Were those flags in this is belongs. And also this app is the most important parameter here to tell to tell us the last of this list. Okay, so with with with this, with this function. So the production of this flux operator like this.
Cong Zhang: Can be be noted at this. So if we didn't. If we didn't, the cares so to get back to the value of this Oliver key and under the under where this key is. So, this equation.
Cong Zhang: Can be can be right like this.
Cong Zhang: So we can see the left hand side is the commentator between this Noemi and and the flax operator. This and the in the right hand side, we didn't care about this. Some over k. So, we will get this.
Cong Zhang: So the first. The first is a production of those flags operator of last am Mayra Swan and then we have a tall. And so this tall is so there is a flux in this is of last one in this tall and then there's an army and also for this, for the second term.
Cong Zhang: Of course,
Cong Zhang: Balance way to this, we lost some information. But I will say that it doesn't matter because, finally, we need to computer the readout by some by this venue to compute Assam over this key and also the value of Africa, so
Cong Zhang: So this is the point. So, let us let us let us. So now that has a son to this some some Elisa of flats in this is of value there.
Cong Zhang: Okay. So as of him, as I mentioned about. So for those for those flags operators, they are Lister can only content at the most, one plus one hour, Matt. Matt Van Man as well so
Cong Zhang: So so so they are like a focus there are like three cases. So now we can see that that all of those flux in this is belonging to the
Cong Zhang: Belonging to the flax. Operator, are there and then we create another in this is, which is the flax in this is belonging to this tall. So with this Oliver Oliver is an abstract index and then we can see they're all permutations of the unit of this to index.
Cong Zhang: And all possible values of this alpha. So, they will finally recover all possible all possibilities of the of this of this of the old regional flax indices, why we do this. So the point is that falling. So again, can see the consider Lighthouse can see that the first term.
Cong Zhang: So we can see if we want to compute the expectation value of the left hand side, we can compute the expectation value of the of the right hand side and the folders.
Cong Zhang: Expectation value of the right hand side. So the expectation value is depend only on the, on the, on the in on the index of this in the P of this one. Okay.
Cong Zhang: Because, because this because the value of the Alpha and the position of this alpha only a factor the, this, this, this, this, this, this overall numerical factor.
Cong Zhang: Okay, so here we can compute the expectation value wise and then we use this procedure to recover the original flax index and the with this recover the original flux index, they can compute all possible values of the numerical factor for very rare cases here.
Cong Zhang: So here it is true, like like
Cong Zhang: The lack of this numerical value only depends on the, on the, on the value of Oliver, but again in this, in this case of the in the case of the Hamiltonian operator. So the overall factor.
Cong Zhang: depends also on the tradition of this alpha among those among those, those were so and then we just did some over this values and the multiply the multiply the eight with the with the expected value of the operator. So we can get the final result.
Cong Zhang: Okay, so
Cong Zhang: So so so this the about at the two point of our algorithm and a visit by using those by using this this this algorithm. So we implant main way computer that expectation value of the Hamiltonian operator. So this is the result.
Cong Zhang: So it is shown again. So to complete my presentation. So we also. We also an ally says a little bit about the effective dynamic driven by this
Cong Zhang: Driving by this effective Hamiltonian. So the model we use is is is the model of gravity, coupled with a mass last color field. So there's mass last color field that is denoted by p
Cong Zhang: Okay, so we can see that this is the this is this is the this is the effective dynamics, driven by this d rose order Hamiltonian and this blue why
Cong Zhang: Is this dynamics trial and by this driven by this this this readout with leading older correction, so, so, so, so
Cong Zhang: So the point is is that, so there are like a to bounce by this leading order correction.
Cong Zhang: And that this result. So, and to be honest, it is true. So because we just gather readout of the expectation value we didn't
Cong Zhang: Understand that this without this without very much but this without So remind me, the results are given by
Cong Zhang: Using human gamma and that in some young in 2000 and not about the cyclic universe model in which they can see the next two leading order correction Loop Quantum cosmological model, but here we didn't see the sack Laker universe. So there is only two pounds.
Cong Zhang: So finally, let me can glue the my work and give some out loop. So we develop an algorithm to compute the expectation value of that actually operator with respect to the team and CO hosted
Cong Zhang: And by using this algorithm we computed the expectation value of the Hamiltonian operator with respect to the homogeneous and as a topic coconut state the readout up to the next two leading all the correction is up tender.
Cong Zhang: And we can do with this code, and we can do something further the first that is to study the effective dynamics to see his religion with the new basking in Luke quantum cosmological model.
Cong Zhang: And also, as we, as I mentioned about, as I mentioned before that this algorithm can be applied to other symmetry reduce the modal like a black hole model or other banki type of cosmology cause Maltese
Cong Zhang: Another another point.
Cong Zhang: Which am interesting is, is to compute the magic is element of the Hamiltonian operator to study the quantum dynamics to see if the effective dynamic and a quantum dynamic in the full loop quantum gravity theory match with each other.
Cong Zhang: Okay, thank you.
Jorge Pullin: Any questions.
Jerzy Lewandowski: The advantage for for the
Jerzy Lewandowski: Our understanding of the food theory of very exact calculation of expectation value of Hamiltonian. I would rather be interested interested interested to know what is evolution generated by Hamiltonian. So what is the commentator of Hamiltonian with some observable rules.
Jerzy Lewandowski: To see if those observable evolve. According to to the classical engine equations to the zeros older and then to see what are the corrections in their evolution in higher orders.
Cong Zhang: Yes, yes. So
Cong Zhang: So, so for for for what you for what you say that does now. So I have some so, so, so, actually. So for this team as coconut state there are this they are this theory them.
Cong Zhang: So they are this theory which which ensure that for this leading order so so so first we can compute the the evolution by using commentator
Cong Zhang: By using the commentator and then compute the expectation value of this of this commentator and the second is to can see the post them bracket between the expectation value of the operator of
Cong Zhang: The posts on bracket between the between the expectation value of the operators. And so, so, so there are this period period which ensures that for leading order. There's two readout i equal to each other.
Cong Zhang: About batter, batter, but you're right that that so we can so so so we can use. We can use the
Cong Zhang: Our algorithm to computer this this this quantum fraction that means to compute to can see that the communicator and then come computer that expectation value up to the age, but other
Jorge Pullin: Other questions.
Abhay Vasant Ashtekar: Yeah, I just, I just had a couple of questions. One is, so in the calculation that you have done finished. Is it
Abhay Vasant Ashtekar: By by construction, so to say, with the lattices, and so on. Is it like the moon not scheme or what if I just kept the first of the leading order and not the sub leading order. Do I just get the me not answer so
Cong Zhang: Yes. So here, so yes, here we just get this mew not scheme. OK. OK.
Abhay Vasant Ashtekar: The second question was that in the next slide. When you are these bounces what what do you know about density is that the two buses are. They're very different from each other. They're about the same. What is the value
Cong Zhang: The way didn't know, so, so, so, so the point is that it's a way just to get a readout of the expected expectation value and the weighted in a study that much on this.
Cong Zhang: On this, on this evolution, like what you mentioned that the density. The density or something like that. But that will be our, our next work.
Abhay Vasant Ashtekar: But, but your slide here says this little sort of mutation. So this plots are not results of a competition.
Cong Zhang: I'm sorry.
Abhay Vasant Ashtekar: This, this slide. The title is results of our completed.
Cong Zhang: All. Okay, yeah. Yeah, so, so, so, so it is true. So, okay. So this slide is just to show some some some like at the beginning of our competition.
Cong Zhang: So, so yeah, so, so, so, so we didn't the study that the details like the density of matter or something like that, at a passport. Awesome. So, so, so, so, so, so, so it is true. We didn't have that much understanding on this readout.
Cong Zhang: So, but this without is true. So this is crack that this without is cracking the we just didn't understand it very well. Now,
Abhay Vasant Ashtekar: Okay, thank you.
Ivan Agullo: I have another question related to this.
Cong Zhang: Okay.
Ivan Agullo: And i mean i apologize because I have some technical issue and I missed the beginning of the talk. So sorry if I ask something that you have already explained
Ivan Agullo: And so looking at these plots. I understand that the difference between the two cars is that in when you are adding you know the the next to lead in order correction in in in in each bar right
Cong Zhang: Yes, yes, but
Ivan Agullo: But, you know, we see a dramatic change between the two. So that's it means that we cannot trust this expansion at all because you know if you introduce the next to next lead in order that result could change completely
Cong Zhang: I ok so the point is that, so, so, so, so, so, so in order to show the in order to show the, a factor of the next two leading order they choose a very large parameter t
Cong Zhang: But if this parameter t is very small then. So the second bounce will be very, very far from the, from the, from the, from the first bounce. And then, and then we can see that this, this, so they are actually much
Cong Zhang: At least
Cong Zhang: Around the bounce or something but
Cong Zhang: But but but i don't know i don't know what will happen if he can see the next to next to live in order so
Cong Zhang: So, so I can, I cannot answer your, your question.
Muxin Han: So,
Abhay Vasant Ashtekar: Continuing the same question why
Abhay Vasant Ashtekar: What is, what is the meaning of this particular value equals 0.2 if I put equal to
Abhay Vasant Ashtekar: You know, much smaller, much larger our get much bigger deviations are much smaller deviations. So what is it that tells you what value should put physically
Cong Zhang: Okay, okay. So I think it relates to the to the definition of this of this tea.
Abhay Vasant Ashtekar: Yeah, so
Cong Zhang: So, so, so, so we can think of this A is the skill, they have their of our experiment and this LP is the is this. Yeah. Our POV mean we know what it means. So, T is the parameter between these two skills. So if t is very, very small, that means to me up there that experiment.
Cong Zhang: In very, very large scale compared to the content scheme.
Abhay Vasant Ashtekar: But what does it mean in the cosmological context.
Abhay Vasant Ashtekar: What is a microscope, boys. The scale at the cosmological it's unfortunate to call it a because he has nothing to the scale factor.
Cong Zhang: So A is just a classical
Cong Zhang: So, so, so, so, so, so kinky. I'm sorry. So, can, can you repeat again. Yo, yo, yo.
Abhay Vasant Ashtekar: Yes. My question is, this is a formal definition that yeah into the system scale a
Abhay Vasant Ashtekar: Yeah, what would be the correct appropriate scale in the cosmology.
Abhay Vasant Ashtekar: To answer the physical question you want was asking in cosmology.
Abhay Vasant Ashtekar: What does. Yeah, same question about what does it mean cosmology.
Abhay Vasant Ashtekar: Physically
Cong Zhang: I think it depends on
Cong Zhang: Okay, so as my understanding, I think it depends on the on the skill we do our observation.
Muxin Han: So, so maybe I have a comment on this. And so for this a me for relevant for cosmology, you can just choose the cosmological constant A
Abhay Vasant Ashtekar: I can't hear you. You have to speak louder.
Muxin Han: Oh, OK. OK, hear me.
Abhay Vasant Ashtekar: Not very well, but okay.
Muxin Han: Oh really. Oh, OK.
Ivan Agullo: I can get the machine.
Muxin Han: Oh, we
Muxin Han: Don't know why.
Muxin Han: I can't tell you here now.
Abhay Vasant Ashtekar: Is better
Muxin Han: Okay, it's fine now.
Abhay Vasant Ashtekar: Yeah, good.
Abhay Vasant Ashtekar: Okay.
Muxin Han: So, so this I mean for in case of cosmology. You can you can simply it said, A to be the radius of the cosmos go constant
Muxin Han: So, so, then in that case. Oh, it's like
Abhay Vasant Ashtekar: You know,
Muxin Han: Yeah, so in this calculation, we don't. But, and it is, it's just because it's so easy to have this term.
Muxin Han: The customer to constant term is just the lambda times volume. And so the quantum correction is just the quantum correction of volume operates. So it's just you to, to put it there. So that's why we yeah we can add it in right away. So that's why we didn't really present that
Abhay Vasant Ashtekar: But if you know
Abhay Vasant Ashtekar: If that is a case, then this correction is completely, totally incredible negligible. Right.
Muxin Han: Yeah. So I mean, in that case. So if we only look at a semi classical behavior, the fact the dynamics that later time. Then, then definitely it is
Abhay Vasant Ashtekar: No, no, no. But you are the buyers, right, because then you will be 10 to the minus side or something like that.
Muxin Han: Oh no, by the bounds is not relevant to T because bounds is relates to me but but here we are immune asking so so the bounce is the for example critical density is new times P one over a million times p squared times P, so it's not relevant to t.
Abhay Vasant Ashtekar: I'm sorry. So, do you have an answer about how to interpret this diagram.
Muxin Han: Oh yeah, so the diagram is is like, I mean the left hand side and the right hand side is is like this interface is analog up to this interface.
Muxin Han: Is a little bit deviating from disappear from the plot, you can see but but it looks like this is our face and it is symmetric. It's looks symmetric. So it means that you have to to bounces to bounces. You got the same critical density. And in the middle is is fo W phase.
Abhay Vasant Ashtekar: Bodies money. What is the meaning of key in this case.
Muxin Han: The bad image is
Abhay Vasant Ashtekar: Equal to 0.2 if in fact that put it to be a logical FRANKLIN SQUARE DANCE cosmology cost it
Then
Muxin Han: Yeah, then these two bounces will will have very light very light very large distance so the distance between these two pounds. This is live immerse proportional to T
Muxin Han: So,
Abhay Vasant Ashtekar: Isn't that the on the only effect just
Muxin Han: Cost me
Abhay Vasant Ashtekar: Very close to each other. It is very, very small.
Muxin Han: No, no, it will be better.
Muxin Han: Ever army.
Cong Zhang: For me, either.
Muxin Han: Yeah, he goes to zero, the distance is infinite.
Muxin Han: So you see the effect of p is it's important at a time. So if you evolve from FR W too late time. Then, in case you have a little bit of tea, then it will bounce back, it will read collapse the universe will read class.
Muxin Han: Only if you have a little bit
Muxin Han: But if you have exactly zero t, then you don't
Muxin Han: You see this T. Is this a little bit critical. So this is something maybe interesting
Cong Zhang: Yeah.
Ivan Agullo: So,
Cong Zhang: The key is zero. So we just go to this H zero and then we can we can we can imagine that. Is this the second bounced is at infinity is at minus infinity and then
Simone Speziale: Can I or
Muxin Han: I'm, by the way, though I have a again. I have a little comment.
Muxin Han: To to to your next question. So because you were talking about the commentators and but but from my understanding about tones result.
Muxin Han: Yes. I mean, I'm coming from this path into raw formulation and point of view is that what would what I can see from from his calculation is, is that what he compute is actually the next order next to leading all the correction to the action. So, which means
Muxin Han: What compelled, is it is part of the next Houdini order correction to the equation motion.
Muxin Han: So this is again right very relevant. It offers right very relevant to the to the to the dynamics of the of the theory.
Jorge Pullin: You monitor your, raise your hand.
Simone Speziale: Yeah. Yes. Thank you. Yeah, I have two quick questions. But first I'd like to see them really impressed that you can do these medical approach to these type of calculations. I think that's really interesting. And it's very good.
Simone Speziale: My question was are using the inviting Cohen states or just the Nandi Giovanni
Once
Cong Zhang: That does
Simone Speziale: He sees all sorts of bleeding orders. If you take into account the projector.
Cong Zhang: So here they use the key variant coherent state, it is not getting environment, but I would like to say that in this in this in this in this new paths integral formulation of Luke quantum gravity. So it doesn't matter. So if this if this current state is
Cong Zhang: Getting environment. I'll get violent
Simone Speziale: Because you have some projector. That takes care of that.
Cong Zhang: Yeah. Yes, yes, yes.
Okay.
Simone Speziale: And my other question was related to what we were discussing if you go back to the brought them in, you have shown us that if you take
Simone Speziale: Different families have it kernel code and states of these demon Queen and states where different families. I mean differentials of tea, then the corrections change the expectation values, maybe
Simone Speziale: Not so much. But the correction changes. And so it was wondering what if you choose another family of Cleveland State so together.
Simone Speziale: Instead of just the complexity fairy queen and states or the queen and states would you also expect the differences
Simone Speziale: In these next two leaning over there and submitting corrections and, if so, I would wonder. It's kind of related to the previous question. Like, how do we choose. What is the physical prescription to choose the equation states and
Simone Speziale: How can we extract the results that to some extent that independent of such choice.
Cong Zhang: Yes, you are you are you are right that here we just a cruise. The team as coherent state. And in this framework, a given by machine and Hong Kong Leo, so it
Cong Zhang: So, so, so I think that yeah so but but but but but so so so it doesn't matter to choose which kind of coordinate state, but maybe you are right. If we choose some other kind of a corner status. So the, the expectation value will be
Simone Speziale: Different right the framework can be applied to any family of Queen and states, I'm sure.
Cong Zhang: Yeah. Yes.
Simone Speziale: expectation values may be at leading Gordon may all be the same. I'm just, it's more if you want a conceptual question supposedly turns out that these are bleeding or their orders depend on the choice of familiar cretin states, then how would we do with it. What is the
Cong Zhang: Yeah, I have no idea about this but i but i agree with you that if it was some other kind of coherence data. So the established order might be different.
Simone Speziale: Right, so
Simone Speziale: It wasn't precisely my question. So how do we deal with that. How
Simone Speziale: Can we give it a physical meaning to this dependence or is there a problem. These are questions that I i wonder myself. In fact, I don't know. I don't have an answer.
Cong Zhang: Yeah, so maybe we need to find some argue of some other some other argument to to save each corner state is better or which is more physical the there.
Muxin Han: Well, the answer to your first one is, it's appalling. So if you firstly us you agree that the the past the integral is independent of coherence late, right. So, but the the
Simone Speziale: Web. No, not independent.
Simone Speziale: It can be formulated with any query in states, but there is
Muxin Han: A
Muxin Han: Dependency formulated it can be formulating an accordion state. I'm in case your coherence it
Muxin Han: Is satisfying resolution of identity.
Muxin Han: I can right
Simone Speziale: Now, but if you see independent, it means that he gives you the same value, no matter which Queen city put which I don't think
Muxin Han: largely depend on initial state, your choice, depending on the different final state you for it. Right. And that's only dependent
Muxin Han: So, so, here, here. I'm the of course you use a different coherence day to compute expectation values and then you get different next to reading all the corrections. It's very possible.
Muxin Han: But if you use different set of coherent state. You also get different matter of factor in passing, and also you you got a different one loop determinant
Muxin Han: So that's why I say what he's calculation did compute the part of the
Muxin Han: Next reading order correction in the quantum dynamics. And there's other part, which are the major factor and also the while loop determinant. So, and those and those combined together will will be the same at the same level dependent as the past in Google formulation
Simone Speziale: Right. Because, because you're saying that point, it will be just the resolution of the entity that you could be doing with any
Simone Speziale: Yeah. Yeah, that's right. But then also the dependence on t should disappear because also the resolution depend of the identity is valid for any tea. So your argument should also apply to the dependence on Tina.
Muxin Han: Well, but I'm you in case you analyze your passing through wrote by using productive expansion with back to a company constant and
Muxin Han: Then you're you're doing inspiring and depending on the company constant
Simone Speziale: So you feel look at financial during key then is not so clear that things will be independent of the choice of
Muxin Han: Family of cohesion, so if nothing is clear. Nothing is clear, but but but I'm what I want to say is that certain dependence will be kindly between the major factor and and the next would even older explanation, but
Abhay Vasant Ashtekar: But, but someone has question was precisely about the fact that you did truncate it to order it, and then it does depend on the choice of states. And I think that's what everybody seems to agree now.
Abhay Vasant Ashtekar: It's
Not a match.
Muxin Han: If you take into account the major factor and and and the
Muxin Han: Determinant from the path and because because from the passing through number web from the passing through the passing through or depend on the parameter t
Muxin Han: Yeah, and T is a parameter in the past, in the past, integral Japan down the choice of coherence, they'd only through the initial state and final state and
Muxin Han: It doesn't depend on the choice of cocaine state in the in the intermediate steps because you some over all the cookies days already
Muxin Han: So then if you take into account all the perturbation all the productivity corrections at all, or tea from the passing through, and it should. It should depend on the Pokemon state at same level as the past in Detroit itself.
Muxin Han: So, so, yeah. And so what I that's why I expect that if you take into account one loop terminal and also metric factor and the next reading order computation will only depend on the
Muxin Han: Effect to the quantum dynamics were only depend on the choice of coherence days through the initial state and final state, not the choice in the middle. But of course, it is my expectation. So, and it has to be proven River.
Abhay Vasant Ashtekar: The second thing was that in this plot that is up there. Our present branch that would think about physically. How are we thinking about the present branch being
Abhay Vasant Ashtekar: Being after this so called second bounce.
Cong Zhang: Maybe we are we are here now.
Abhay Vasant Ashtekar: Oh, so it's not
Abhay Vasant Ashtekar: So it's not near where the so the other balance is completely something. So, uh, what is it that tells you where where we are.
Abhay Vasant Ashtekar: I mean, why can I say that I'm in the future brown on the right hand side branch.
Cong Zhang: Oh ok ok ok ok so so okay so the point is, like,
Cong Zhang: If, if their evolution is this direction. I'm sorry. So I just think that the evolution time if the evolution is
Cong Zhang: No, I think we are here.
Abhay Vasant Ashtekar: We should action is a religion. It is increasing or decreasing
Abhay Vasant Ashtekar: This is, in fact, increasing on the scale factor because
Cong Zhang: This direction this down because the here. Is this like a sitter approach and here is this fri W approach.
Cong Zhang: And so we should we should. So if we didn't consider this this this next to living next to leading order correction, so why should they, why should it be in this branch, they should be in this branch. And so here
Abhay Vasant Ashtekar: So sorry. So as you're going to the left hand side, the scale factor is increasing their universe expanding or is it
Cong Zhang: So, so, kick, kick, kick a repeat again.
Abhay Vasant Ashtekar: Yeah, if you are going to the left hand side.
Abhay Vasant Ashtekar: Is the universe expanding or contracting
Cong Zhang: Expanding expanding
Abhay Vasant Ashtekar: So then, so that then there is a bouncer the last one.
Cong Zhang: Yes, so this
One.
Cong Zhang: Yes. Yeah, saying,
Abhay Vasant Ashtekar: So your prediction is that somehow classical general attitude is violated.
Cong Zhang: At some. Yes, exactly.
Abhay Vasant Ashtekar: For the current quarter corrections are large and what one would normally think of as being classical regime. Is that what you're saying.
Cong Zhang: Um, so, okay.
Cong Zhang: It's not
Cong Zhang: It is not
Cong Zhang: Okay, okay. Please. Please.
Cong Zhang: So so so my point is that it is also very stringent for me. And we need to start at eight, but this readout. It is shown by the
Cong Zhang: Bias solving the solving the equation of emotion and it is, it is true, like if we can see that this correction. That means like a, we will have another bounce in this large volume area.
Abhay Vasant Ashtekar: Yeah, so I know I understand which paper you're talking about this deal my paper at a similar thing and we know what I understood how that would happen. Yes, a large volume.
Abhay Vasant Ashtekar: Yes, or density at low curvature there is a bombs that
Cong Zhang: Varies by there is no traction so it is
Abhay Vasant Ashtekar: Most people were then
Abhay Vasant Ashtekar: Just say that your content is wrong. Right. And because how can you kind of tell you say that there are large effect not just small or large fish quality large effects at lower densities and local churches.
Cong Zhang: But yeah
Muxin Han: Long time, right. It's a accumulates more small quantum effect for a long time.
Cong Zhang: Yes, yes, yes. So, so, so, so, so, so from our from our physical understanding. So, it is it is understandable, but
Muxin Han: That and and i mean in case t is very small. So this, this time is is even like really really long.
Cong Zhang: Yeah, but it is also like a very, very
Cong Zhang: Large man.
Cong Zhang: This
Abhay Vasant Ashtekar: Yeah. So you're saying that locally. The curvature, you're saying that, then whatever long time. Whatever reason still say that therefore activity loca witches dynamics can be very different extremely different from classical general attitude. Yeah.
Muxin Han: So we sing song already said, and it is just the new not scheme so
Muxin Han: It has other problems as well so
Abhay Vasant Ashtekar: Yeah, that's to get a lot, so maybe it is an artifact of the meaning of scheme. Right. But I don't think I would buy that.
Abhay Vasant Ashtekar: That very local which is even if you wait for a long time. Doesn't matter where what a park in the history of the universe. If you try the quantum theory is saying that at local, which is low density is there's a quality difference from
But
Abhay Vasant Ashtekar: I would not buy that.
Cong Zhang: But I have another so, so, so, so, so I have another idea about this, about this picture, but I just, I just don't know.
Cong Zhang: If it is true. So the point is, like, if we can see there, if we can see the here. So the universe, like so, first expand and then
Cong Zhang: And then go back again. So that means like there is there. So, this effect. So, this this E factor is looks like that there is a there is something like a negative negative customer cosmological constant. So, so
Cong Zhang: But if we can see the if we can see that the readout from the quantum field theory, there is this there is this like a vacuum energy, which will provide
Cong Zhang: A positive polarity cosmological constant may be
Abhay Vasant Ashtekar: Now what this has to come out of content on gravity. You cannot say that I got a liability and I'm going to supplement with contemplating code space types that just seems
Abhay Vasant Ashtekar: weird to me.
Abhay Vasant Ashtekar: This is, this is my just
Abhay Vasant Ashtekar: Places, but that either don't understand. It doesn't mean anything more than that. Thank you very much for your explanations both machine and calm. Okay.
Enjoy.
Jorge Pullin: Hand up for a while now.
Gioele Botta UW: Yes, I have a question tsonga. Can you go back to this slide of coherence states when you show the properties of P goodness
Gioele Botta UW: Here. Yeah. So you said that these are basically the remote extracted quality and they are valid in like some limit where some parameter is go to going to zero. Right.
Gioele Botta UW: Yes, and which parameter is eat.
Gioele Botta UW: So what does it mean that if I'm going to next to the leading goal of this property of bigness are not preserve
Gioele Botta UW: Because it's the same T of your expansion. This one.
Simone Speziale: Right, you have corrections enlarge eater, even if these more but you take a minute to eat, you will not get, for instance, you won't know not even be linear in either the expectation. Well, you had
Gioele Botta UW: That that's my point. So, right. So what does it mean that
Simone Speziale: What it is well known property they in fact Thomas says, only the ones we large Geeta should be considered really semi classical
Gioele Botta UW: The fame, because
Simone Speziale: As a family acquaintances includes them all, but those that have seen because he got properties, only those that describe large areas. This is the
Gioele Botta UW: Yes, and that's why I was wondering. Oh, you can trust this I mean this states at some point when you are going to hire or they're empty.
Simone Speziale: It's tricky to do better. We do better.
Gioele Botta UW: I agree I
Gioele Botta UW: agree. I agree. But I mean,
Gioele Botta UW: I'm not saying that I want to do something better now. But I mean, my problem is, how can I trust the next to the leading order calculating on the stage justice.
Cong Zhang: But, but I did so, so, so, so, so, so, and I know your classmates. That's why, but I didn't get the point of your question, so why we couldn't believe this.
Gioele Botta UW: Because you i think that you need these properties to your calculation. I mean, that
Cong Zhang: No no no they didn't know they didn't need this property.
Cong Zhang: Okay, yeah, yeah. So, so this is not, this is not a kid. So actually,
Cong Zhang: Yeah. So yeah, we didn't need this property so
Yeah.
Gioele Botta UW: I mean, but how can you be sure that your current state or pecan the right. I don't know. Friedman metric or something like this. If you this property doesn't hold
But
Cong Zhang: Ok ok ok ok so I think the point is, like,
Cong Zhang: The point is that so so this this like FR W cause Modi or something like that is defined in this luxury region and
Gioele Botta UW: In this. Yeah, I agree.
Gioele Botta UW: But
Cong Zhang: Yeah, this is cracked the folders large eater. So, so I think it will be fine.
Gioele Botta UW: Yeah, exactly. But this way when you go to the next reading or there is not zero anymore. Somehow, because you will say that you can compute any any next to the reading order at some point that will matter that's what's related
Cong Zhang: All you can say, or another. Another point is that, so if you choose a parameter t if you choose a parameter t. And so there will be some area that so, so, so, so that means that this eater should be relatively large Daniel. Daniel parameter tea.
Gioele Botta UW: Okay, so it was okay. So, okay, they're receiving this email to considering the game.
Cong Zhang: Okay, yeah, yeah. If you choose some fun at the tea and this he goes to their proposal. Yeah. Is there, there will be something
Gioele Botta UW: Okay, so there is even the limit of keeping them. Yeah. Okay.
Jorge Pullin: So Europe, you have your hand.
Jerzy Lewandowski: Yes. So thank you for addressing my question on the in quantum constraints. However, I'm still not not satisfied by the by the answer so
Jerzy Lewandowski: So you say that in your approach, it doesn't matter whether state satisfies quantum constraints or not. And you still can extract some physically relevant number from from state which does not satisfy quantum constraints.
Cong Zhang: Yeah, I think it is something related to the
Cong Zhang: Okay, so, so the point is, like, in general, I think we should can see that the key to the environment, the current status of the beach satisfy the coaching.
Cong Zhang: Constraint or something like that but but in this framework. So, which is given by Musi handles.
Cong Zhang: So it doesn't matter if this coherent state is Katie environment or not. So, so they will get they will finally Bye bye, very bad by by using this effective action so they will finally get some some equation, which means
Cong Zhang: Which means that beta is equals, which is equivalent to the caution constraint and the different more freedom constraint.
Jerzy Lewandowski: Right, but I can, I can imagine that you start with arbitrary state and you
Jerzy Lewandowski: Buy some reading maps, you turn it into a solution of constraints, but then you lose something. And if you start with a constraint we with
Jerzy Lewandowski: State, which actually is a solution to quantum constraints, then you lose zero. But if you start with a state which is far from being a solution to quantum constraints. Then after projecting you you get only only very little. So this should affect your numerical
Jerzy Lewandowski: Value which numbers which you obtain for expectation for for for for
Jerzy Lewandowski: an expectation values for for for your observable because you calculate expectation values of this part of state which which is not physical.
Jerzy Lewandowski: So I believe that you can have a framework in such that you drop in any state and it produces it makes it solution. However, I believe in expectation values of
Jerzy Lewandowski: State before it is treated with some region map which turns into into a solution to quantum constraint.
Cong Zhang: But
Jerzy Lewandowski: I think the point
Jerzy Lewandowski: Is other framework where they just cannot imagine this.
Cong Zhang: Happen. Yeah, but, but I want to see.
Cong Zhang: Something others like
Cong Zhang: So for instance, for this current state it is labeled
Cong Zhang: By some power meter and and as my understanding. So, so for some kind of current state if you if you project that them to this.
Cong Zhang: To this kitty environment, the space. So, you will get nothing but but if those state of if those data to label the corners data satisfy like a Goshen constraint.
Cong Zhang: So, so, and then you do the projection for those for those kind of coordinated so you will get to that the the the prop that is peaking property will still be preserved by for such kind of coherent state.
Simone Speziale: Right. It is a subleasing effects usually
Cong Zhang: Just means
Simone Speziale: The only table. There is a good environment is eat. Of course, all the others or not.
Cong Zhang: But, yeah, yeah.
Yeah.
So,
Muxin Han: I have a comment on that. So your question. And so the
Muxin Han: The concern you, Rick raised and we really as it relates to the statement I made
Muxin Han: Earlier that I'm songs calculation only capture a part of the quantum correction, not all on correction, because the corner director in the passing through also come from macro factor and one loop.
Muxin Han: Determine at this one. Look, determine and actually part of the one Luke determinant is from the group every
Muxin Han: So, so that part. It's, it's
Muxin Han: Related to the gauges. So this calculation. You don't see this part. So it's not applicable and it's it's also relates to up is concerned earlier a concern about this to bounties and and so the
Muxin Han: Two. To clarify our altitude out this calculation. Is that what I'm this this is
Muxin Han: This just a demonstrate what we can do to compute these Hamiltonian constraint operator and and to relevant to the physics.
Muxin Han: You I'm you have to take into account all the quantum corrections. And so these these calculation only captured a part of the functions. And the other part of
Muxin Han: The corrections in the dynamics, which we haven't taken account yet. So I'm in this diagram is just a presentation purpose to illustrating
Muxin Han: The difference between the leading order dynamics. Rom. This part of the quantum correction, but
Muxin Han: The altitude is that it's not the cool part. Yeah.
Abhay Vasant Ashtekar: It's not the version I think thank you very much for this comment because I was thinking that this is what's your attitude was
Abhay Vasant Ashtekar: But I was not sure. I mean, it's good to hear it straight from you right that yeah I completely agree with this attitude that you know
Abhay Vasant Ashtekar: It's a very hard problem. Let us make simplifications. Let us be able to calculate things later screw this theorems we simplify the computation time reduce the computation time enormously and then add all those more realistic.
Abhay Vasant Ashtekar: Issues like this memoir factor and then
Abhay Vasant Ashtekar: The major factor there and so on so forth.
Abhay Vasant Ashtekar: So I think with this attitude I completely agree that this is very, very nice. And it's also as similarly said extremely non trivial that one can calculate all these things.
Abhay Vasant Ashtekar: So I thank you for saying this because I was hoping that your attitude. So that's very nice for me to hear that from you. Thank you. Thank you.
Jorge Pullin: Any other questions.
Jorge Pullin: Okay, that's fine Kong again.
Cong Zhang: Thank you.
Jorge Pullin: Happy Holidays and see you next semester.