Jorge Pullin: Our speaker today. He will speak about the status of group up
Daniele Oriti: Yeah, so thanks for thanks to everyone for being here. I guess you have to stay home anyway so better use the time for public so so I was asked to give
Daniele Oriti: An overview of the status of tearing. So this is what I will do
Daniele Oriti: Can you hear me okay and see the slides and everything he is back so
Yeah.
Daniele Oriti: Okay, good. And saga.
Daniele Oriti: Okay, so I will first introduce a little bit before my just to put people on par with the what I'm going to say in the following
Daniele Oriti: And then I will review a number of results, each of them very briefly, and I'll divide the overview in three parts. So some results are just about the formula asthma and the foundations of the formula. There's no
Daniele Oriti: Then there is another number a vast number of results, having to do with the consistency of the former asthma and the continuum limit and then a number of directions. There is other directions aiming at destructing effective continuing physics from the formulas
Daniele Oriti: So let's start.
Daniele Oriti: So go figure it a few theories as most of you know, and they're not defining space time as it isn't necessarily the case is they want to explain space time as any to your quantum gravity should
Daniele Oriti: And they as a first definition there quantum physics theories over a good manifold.
Daniele Oriti: The relevant classical face space is the conundrum bundle other a good manifold that that is you can also formulate them on the corresponding the algebra is a contract with variable.
Daniele Oriti: Set the variables and then the parameter d, the number of copies of the group has to do in the models which are most relevant for quantum gravity with the dimensions of the space time you want to reconstruct
Daniele Oriti: From the models and the group, but in the same classroom models is chosen. Normally, it will be the local group of gravity.
Daniele Oriti: The format is not is more general and we'll see variations of this
Daniele Oriti: basic ingredients in the following
Daniele Oriti: So in the models that are directly to do with the quantum gravity, and in particular we loop on to gravity is being formed. So there is the basic
Daniele Oriti: Very simple way of understanding the type of ingredients which are used, though, which has to do with the
Daniele Oriti: Single quanta the individual quantel the field.
Daniele Oriti: In this models which are supposed to represent geometric data here.
simone: Hello. Are we still live in more
Jorge Pullin: Than nearly we seem not to be able to hear you.
simone: Then you can use the chat. Just to let us know if you have a mic problem or something else.
simone: On the bottom of the screen you have access to a chart if you
Jorge Pullin: I sent him a message, but I don't know if he's saying
simone: Well anyways, he's sharing his screen screen has not changed.
simone: So he probably is not going ahead with this talk.
simone: Yeah baby rebooting.
Jorge Pullin: Wait for a second.
Daniele Oriti: Okay, good. So I think here is where I left off.
Daniele Oriti: So we can describe the geometry of a single day trader on as people doing spin for models know very well with the using for vectors corresponding to the normal, sir, to the triangle. So the boundary of the trader.
Daniele Oriti: subject to the constraints that they have to lie on the same on a given IP surface identify with the normal and that they have to close.
Daniele Oriti: Now an equivalent. The description is in terms of the area two forms.
Daniele Oriti: And they are subject to the simplicity constraints, as we know, and the tour equivalent
Daniele Oriti: And thanks to the constraints constraints imposing bookcases they suggest to us as a random on facebook page equal dungeon bundle of the four copies of the Lawrence group or equivalent Lee with the thanks to the constraints for copies of the rotation group.
Daniele Oriti: And that is, of course, can be generalized the conundrum bundle of an arbitrary groups regroup and arbiter number of dimensions, the corresponding healed the space in group variables will be the square interval functions of other the group.
Daniele Oriti: To which we we add that the relevant constraints or equivalent to you can go in, in the US, the algebra space and I've been on Community functions of the algebra.
Daniele Oriti: The
Daniele Oriti: The dynamics for this type of models is
Wait. OK.
OK.
Daniele Oriti: So the dynamics for this type of model is designed so the describes the grooming processes and the formation of extended these key structures, starting from these individual building blocks.
Daniele Oriti: And therefore the simulation model. So the interaction process will correspond to simply show complexes
Daniele Oriti: In order to do that, that the interactions for this for the fields that are created an articulate this quanta should be no local in the sense that the arguments of the field. So in the introduction to repair that
Daniele Oriti: In a, in a certain community or a pattern in this case, same four dimensions that is the convenient or a pattern of the gluons. Of the five to try drawing the boundary for simplex
Daniele Oriti: In general, you're going to have some interaction which describes the fundamental building block fundamental space time cell and then a kinetic term and therefore propagator that will describe how you blew the fundamentals based themselves across the lower dimensional faces.
Daniele Oriti: And again by construction, the moment to sum up some you expand the theory in perturbation expansion around the simple vacuum around the free tier, and then you have some over tribulations or or complexes weighted by some amplitude
Daniele Oriti: The final diagrams that is correspond to sell your complexes
Daniele Oriti: Now first point.
Daniele Oriti: Of contact with other formulas. You may have seen is a simple reduction of groceries theories to tensor model. So when you obtain when you just
Daniele Oriti: Replace the group, but with some finite group or some finite set, you still have a tensor but Andy convenient Oryx is unchanged that but of course you lose all the group erratic data.
Daniele Oriti: The consumers that the quantum dynamics, it becomes a purely conspiratorial
Daniele Oriti: In particular, the quantum computers for each find them diagram for each cell you are complex or just a function of the compassionate Oryx of the complex itself and whatever parameter you add, for example, the dimension of the tensor indices
Daniele Oriti: Now you can also include curious, you can bring to the forefront of distance Oriel aspects of the story, in particular by requiring that the option should
Daniele Oriti: possess the environments under the sun unitary group acting under the indices, the arguments of the fields.
Daniele Oriti: And if you do so, then there is a well defined and very large theory space in which all the possible interactions are labeled by what are called the color bubbles. So anyway, there is a restricted.
Daniele Oriti: Class of combine authorial patterns. You can choose for your interactions.
Daniele Oriti: We will see this type of models in the following
Daniele Oriti: Thanks to this to the fact that the community structure remains the same intense or models by in a much simpler context that a large number of results have been obtained and imported in Greenfield Curie.
Daniele Oriti: Starting from this purity can be not already set up in particular, we know that if you want to encode the topology, or the full cellular complex
Daniele Oriti: In the diagram. So you need the colors.
Daniele Oriti: And this could be useful. Also in the context of a spin for model. So we also know
Daniele Oriti: That this models processor was defined large and expansion, the details. Maybe depends on the specific models, but for a large cluster models, what happens in the larger than. So when the dimension of the indices
Daniele Oriti: Grows is understood
Daniele Oriti: In general, one point of interest, at least in my view of goofy curious that they're related to a number of other formulas. My already mentioned tensor model set, but of course we are here because we're interestingly pumping gravity.
Daniele Oriti: And spin for model. So let me sketch what is the relationship of goofy curious with the loop on gravity, the relational and the differences
Daniele Oriti: So the hubris pace of the few theories and adjust introduced, there is a fox base. If you assume was only statistics, then it's going to be just the symmetric tensor product of the one particle or single quantum he'll be space I introduced the previously.
Daniele Oriti: So it's a standard Fox base. So a generic state is going to be some collection of the trade route or do you only a collections be natural vertices
Daniele Oriti: Labor by their group direct data I discussed among those are there, there's going to be the states are corresponding to the cases in which were glued together.
Daniele Oriti: The trade route to form extended structures and you glued together these be Napa vertices to add spin that those dates for closed the standard graphs.
Daniele Oriti: You can write down the second contest or presentation for the stage, but also of course for geometric operators, including dynamical wants like any candidate Hamiltonian constraint, once you write it as acting on this Fox base.
Daniele Oriti: And the way you translate from one from the usual description to the second one is a keener the standard strategy for turning into a cycle contest for more is my first one.
simone: I still
simone: When you define these folks piece that you're assuming that they each were confused about the gluing condition on the spins.
simone: Mm hmm. Are you assuming something like that because you're not assuming you don't have Link See It Right. You're just intensive projects or vertices
simone: So don't know yet how do I connected as the
Daniele Oriti: Hub Myspace in this which which means that a basis for states will be given by products but generic states are not going to be products.
Daniele Oriti: Are going to be entangled in particular, and the glued once the state's corresponds to a standard structures or close graph thing, which include the vertices are indeed the ones in which one tangled the degrees of freedom in the tensor product.
simone: So,
Daniele Oriti: Then of course in so you just do the usual gluing of open edges in the networks are by multi by inserting chronic health as on the representations and on the angular momentum indices and tracing
simone: So for these folks piece you have defined as the action of the warm up readers appear is not defined. They will only be defined once you look at these entangled or fluid as you go.
Daniele Oriti: Over that for a long time is over fast that that passion several vertices is going to be a many body operator, but it is defined it doesn't let you have to be careful with the definition
simone: But how do you do. OK, so maybe this will be helpful. How is this, how is the overview burrito defined on these folks, please.
Daniele Oriti: So you have a definition in terms of the action of the safety net of the alarm operator over SP networker processing a new, for example.
simone: Now, but even just a link. Let's make it simple. Just have a synchronous network. I know how the little rock's
Daniele Oriti: Well, you have a multiplicative operator in for each how Flink
simone: Know it's only if they. I mean, okay. But if the alpha link has the same speed as the other half of the week. This is what is confusing me I need that information to make sense of their own operator and in this way of writing it is anyways. Maybe it is not so important.
Daniele Oriti: Okay, we can we can discuss later. Let me go ahead and then we discuss the various operators, I can. I mean, in general, any operator that touches several nodes.
Daniele Oriti: Is certainly more complicated than one body operators like the volume.
simone: So I don't mean that is completed a lot. I mean, did I don't see how we can ever be defined unless you restrict
simone: The unless you give me the information that the links that to have links have the same Spain. But, but, I mean, as I said, Maybe staking is not important for this country. Sorry about that.
wolfgang wieland: May or May I say something, sorry.
simone: Yes, please.
wolfgang wieland: Similar Mona. I think it's as far as I, excuse me, as far as I understand, a construction. It's quite similar to this spinner approach that you have been known to using so much that it's at the level of the
wolfgang wieland: GMT Hilbert space indeed days no Ilana me operator just in the same way as a hollow Noemi
wolfgang wieland: Functional on the in the spinner representation of the T staff as you to face space only exists. After imposing the gluing constraints, but if there are your matching constraints.
simone: Precisely. No, I completely agree it is why I was asking if at the level of these folks PC was not defined unless one for the restricts in some way.
Daniele Oriti: That this means that the long as you want to define it will include the the matching of the spins.
Daniele Oriti: So in general, you're going to have functions of the group data acting on whatever states. And if you are in states which are representing the
Daniele Oriti: Bu variable. So you are in the group representation, they will act multiplicative Lee then you operator you want imposes in practice. Also the gluing
Daniele Oriti: Before acting. Anyway, this is really technical. I mean, and as I said that there is a
Daniele Oriti: Mean it's not easy to define an elaborate on that touches more than one that depends on more than one vertex at the same time.
simone: Then the plan is taken, you go, but it's useful, you know, from a pedagogical perspective, just to
simone: Understand that this is something larger than the usual a brisk pace of Luke on to grab
Daniele Oriti: This is going to say next slide that, that's for sure.
Daniele Oriti: That this is not an issue just in particular with with a specific operator is larger in this definition, it has more states and they are organized differently. Even the ones that are corresponding to close the speed networks are close graphs. They are organized differently here.
Daniele Oriti: Can I
Jorge Pullin: Go ahead.
Daniele Oriti: Alright so let me compare the 200 plus pages. So there are speed networks in both he'll be spaces, in particular the web space for
Daniele Oriti: For speed networks or four states associated with close graphs can be seen as a subspace embedded faithfully in the space correspondent with fixed number of vertices, of course, the same number of the nodes of the graph.
Daniele Oriti: However, of course, is a different space so
Daniele Oriti: For example, you have your tonality in the workspace only four states with a different number of vertices. Otherwise, in general, I'm not going to be orthogonal.
Daniele Oriti: Contrary to what happens in the loop on gravity space and then again at this stage of this new position of a cylindrical equivalence of any type.
Daniele Oriti: This means that you don't have any needed continue interpretation for the states and the operators that are acting here in a sense of the simple social perspective is brought to the to the forefront in this context.
Daniele Oriti: But as I said you can for any state in the
Daniele Oriti: Loop loop on the bus page. You can find the counterpart in the fox space, as I said, the web or the states are embedded differently.
Daniele Oriti: When they correspond to different graphs.
Daniele Oriti: Concerning the relation we speak for models instead. So first of all, let's
Daniele Oriti: Make one clear point, which is that when we talk about speed for models, a given speed for model.
Daniele Oriti: Means the set of quantum computers for all possible simple complex or non traditional complexes. We are we are interested in some particular class.
Daniele Oriti: Last time we have organized in such ambiguous. This could be some refinements or some some the prescription coming from graffiti theory is that you define the spin for malls.
Daniele Oriti: Through some over complexes and this comes from the protobuf expansion of graffiti theory. And the way it works is simply that if you have, if you give me an expression for this before model.
Daniele Oriti: In terms of that is local in the sense that it it has an antidote for the building blocks of the sprint phone complex and amplitude that come from their gluing this corresponds to a choice of the vertex colonel and kinetic colonel and therefore an action for a graffiti remodel
Daniele Oriti: And previous correspondents
Daniele Oriti: follows from this correspondence folders that the given goofy theory model will have the initial sprint for model as the firemen amplitude for its fireman diagrams.
Daniele Oriti: Apart from giving a prescription for the organization principle for the complete definitional spin for model. It's
Daniele Oriti: It's good to have this type of is useful for this type of quantum physics, you're embedding it because it provides a number of additional tools also to also to go beyond the deeper, but he was punching itself. So the standard as informed formulation
Daniele Oriti: Term allaster concerning this relational without a quantum gravity formalism some something else which is quite generic and girlfriends juries, is that the fine line amplitude can be understood.
Daniele Oriti: As discreet gravity locked is gravity path interest. Now this is true, literally, for all models that I know that are based on constrained VF theory.
Daniele Oriti: And you can see when you go to the flux of presentation. So this is the correspondence will let this path integral. So doesn't hold the in the semi classical approximation. He told the full quantum regime, of course.
Daniele Oriti: Something more happens in the semi classic approximation which is usually that you go from a first order action to a second order one.
Daniele Oriti: Now the details of course, depending on the specific model, but
Daniele Oriti: As I said, this statement is quite generic
Daniele Oriti: Then
Daniele Oriti: I've done with the basic introduction to to grow food curious, or at least I should have an idea of the formula if you didn't have it already. And now we started to review partner.
Daniele Oriti: Discussing a number of the developments over the last few years. So first let's discuss things which have to do with the foundations of the formulas itself.
Daniele Oriti: So given that we have a quantum field theory, it's quite important to have some idea of his symmetries for a large as large as possible classroom walls.
Daniele Oriti: So some of the symmetries that had been studied are structural so they are not so much dependent on specific models and they are affected, he can be. Not all features.
Daniele Oriti: So one is the permutation symmetry. This will start at the very beginning of the formula is
Daniele Oriti: 20 years ago, my God.
Daniele Oriti: So we can impose a symmetry of the goofy Curie field on the limitations of his arguments and you can read out an ENCODE the orientation of the fireman diagrams or the formalism, the filtering.
Daniele Oriti: On this invitation symmetry, thanks to display mutations in the drink and control whether you generate Oriental or an oriental complexes
Daniele Oriti: The moment to introduce colors as a sad is useful coming from tensor model. So in order to fully control the topology. The final diagrams on the cellular accomplish which are generated in the body respond to
Daniele Oriti: Them. They spend mutation symmetry is actually dropped it because the colors fix the order of the goofy theory arguments and they can be used to determine the orientation of the diagrams.
Daniele Oriti: And other very general class for symmetries at the structural level again is the sensorial or unitary symmetry. Did I mentioned the beginning
Daniele Oriti: Your pencil field so
Daniele Oriti: You can have a unitary group acting on each argument.
Daniele Oriti: And if you recall, as I said earlier, if you require that interactions have to be environment under these action of the unitary group then you restrict your allowed interactions in a way that usually does not include simply shall interactions.
Daniele Oriti: But you end up with a cluster models that are labeled sensorial because indeed the brink of is sensorial aspect to the forefront.
Daniele Oriti: We're going to see that these are specially started in the content so normalization.
Daniele Oriti: Then there are a lot of special symmetry that have been studied the in models and motivated by quantum geometry. So, the most interesting ones from our perspective.
Daniele Oriti: The first is the local Lawrence or so.
wolfgang wieland: To see my first we can Isla sorry he is working. Just a quick question whether there is a coloring or not. So whether these legs are
wolfgang wieland: So going back to the last slide is related to choosing the statistics. So whether it is the and does this show up in the in the computation relations of the cheeky operator.
Daniele Oriti: Look,
Daniele Oriti: So you're asking where
All
Daniele Oriti: The coloring is affected by the statistics.
Daniele Oriti: Is that your question.
wolfgang wieland: Yes.
Daniele Oriti: Versa where it affects it so
wolfgang wieland: This next
Daniele Oriti: I would say no. But hadn't thought about it. So I don't think so, because the, the fact that the field transforms in a well defined way under this directory group or not is somehow before you even asked what are the competition relations between field operations.
Daniele Oriti: Frankly, I don't see where it would
wolfgang wieland: Go. Okay, no, no. I was just wondering if this has to do with like the different
Daniele Oriti: Statistics in the influence of the specific commutation relations. Once you assume it, but it's not the confidence of that.
wolfgang wieland: Okay, thank you.
Daniele Oriti: Okay, then the local Lawrence or supersymmetry can impose it the level of each field that requiring it to be environment on a diagonal action of the group.
Daniele Oriti: Or in models in which we impose or the simplicity constraints and better way to do it actually is to require covariance of the group.
Daniele Oriti: Domain.
Daniele Oriti: Of the dependence on the field on the group elements under the transformation of them, alongside the normal vector promoted to a variable. This ensures the covariance of the imposition of these in physical strength.
Daniele Oriti: But this is the one known cemetery gates image will be network states and spring for long periods.
Daniele Oriti: And other symmetry that's being studied the is the graffiti re counterpart to the vertex translations that have been also label the simulation different more physical in some additional gravity.
Daniele Oriti: And I have to say that we we were able to identify one such symmetry is a quantum group symmetry that is most manifest in flux variables, but I'm not sure I'm very satisfied with that because it's a particularly we're symmetry from the quantum field theory point of view.
Daniele Oriti: So, um, let's just say that there is a lot to be understood still at that level.
Daniele Oriti: Okay.
Daniele Oriti: Once we are discussing classical singers who the jury, a beautiful curious.
Daniele Oriti: One is natural naturally led the to wonder
Daniele Oriti: If there is a general treatment of classical symmetries.
Daniele Oriti: Even in this no local convenient already know local case. So people have
Daniele Oriti: Asked this question and try to start developing a very generalization of meta analysis to discuss of non local upon two features.
Daniele Oriti: And what way to state more clearly was sent them a local as few years is that they are defined on different direction is a sum of terms are defined each one different vector bundle. It depends on if you want more you recycle unit on and different number of independent group variables.
Daniele Oriti: So you have to generalize the usual nurturer analysis and you end up with a generalized conservation low, which is, which actually looks like a continuity equation to which you have necessarily sources coming from the non local terms.
Daniele Oriti: And we use the this framework to start in a number of cemeteries, including the the previous one. So the local asymmetries of the number of models.
Daniele Oriti: And then, well, once we are at the classical level you can start simply asking that, even before any quantum gravity interpretation. What are the classical equations emotion.
Daniele Oriti: Which are complicated, the integral differential equations or in a presentation variable. They are complicated algebraic equations.
Daniele Oriti: And whether you can find solutions of them. So we know a number of solutions. Some of them are more interesting. Most of them are very simple and not particularly enlightening. In general, I mean, when you just look at them.
Daniele Oriti: From the quantum geometric point of view.
Daniele Oriti: But we're building up some experience in this context to
Daniele Oriti: Then introduce that the the fox, a presentation for this is curious, you can also wonder if there are other representations and you can have
Daniele Oriti: In fact, you will respect that, first of all, that there is a multitude of equivalent representations characterized by different symmetries, simply because we're dealing with interacting quantum filters.
Daniele Oriti: And you will also respect that these unequivocal representations correspond to different containing phases of of any given model.
Daniele Oriti: Then you also suspect that in general, the fox space presentation, should we not exist for the interacting Kira in the full thermodynamic climate.
Daniele Oriti: And this is assuming that. So this is just an expectation, assuming that that there is some more local generalization of the XT or
Daniele Oriti: For a usual a local quantum physics years
Daniele Oriti: And we have studied. Indeed, the other relevant representations corresponding to coherent state.
Daniele Oriti: Of the Bible algebra of field operators in generic new frontiers.
Daniele Oriti: Do way one does. It is again is the analog of the is the parallel of the usual constructions in local quantum filters here in this context the nonlocality is do not seem to present much of a change much of a challenge.
Daniele Oriti: And you find indeed the equivalent coherent state representations with with broken symmetry in the non compact case.
Daniele Oriti: Using the group or as a configuration space.
Daniele Oriti: If you want to find the same type of equivalent
Daniele Oriti: Possibilities. In the case of compact groups, then this will not be obtained using the group as configuration of space, but only need you work construction on the algebra. So switching basically the role of the moment. If you want a configuration variables.
Daniele Oriti: But, but, in general, just like in quantum field years local control features us back in equivalent or presentations and to the extent to which we go the test that the expectation. It is satisfied.
Daniele Oriti: Then start motivated first by cosmology. But then as a more general
Daniele Oriti: question we asked how you couple matter. They were there was a lot of early work in this context.
Daniele Oriti: And the basic idea is that you need to expand that the domain of the roof security fields. If you want to include the map the fields. If you want to include the degrees of freedom, corresponding to Martha fields.
Daniele Oriti: For a single sterile field that extension will be simple. You just add the one we are variable. If you have a real scale field that to the group variables representing the discrete connection.
The connection.
Daniele Oriti: And more involved analysis, leading to a specific proposal for the couple the models basically using the same guidelines that we use in the pool gravity case.
Daniele Oriti: We want to find an amplitude of the model of the goofy during model to give you a simple path integral for gravity now capital to scare of fields.
Daniele Oriti: So you have to study with this a lot. This part into looks like or what are the relevant degrees of freedom and relevant coupling between them, between gravity and the skater field.
Daniele Oriti: And and then you starting from the knowledge of the superficial path Integra you reconstruct the what the vertex caramel and the propagator of the goofy curious should be
Daniele Oriti: And you define the action. So indeed you going sort of reverse engineering it
Daniele Oriti: But I think this is basically what we do also for gravitational models for to gravity months. So in fact, you can show that largely this action is captured by symmetries. And you can simplify greatly keeping the correct the classical and continuum limit.
Daniele Oriti: The naive continually meet. Of course we're not talking about the food quantum dynamics yet.
Western: Nana.
Daniele Oriti: Yep.
Western: Sorry, I have a question. This point can you have to understand the difference between what you're doing with a copy of this color field with respect to what what is done in
Western: Spain for him because he's been form, I expect to discover a few that will appear somehow leaving on the links and you have a structured as see Mona was not seen before in which the links are somehow appear in a second moment. So can you highlight that.
Daniele Oriti: Yes, so the for look at the simplicity path internal
Daniele Oriti: So first of all, I expect the situation to be in fact the sameness been for models.
Daniele Oriti: And we looked at distribution center is the starting point. But one can also simply start with a spoon for model you you you like a couple to skate on fields and reconstruct the corresponding graffiti curing following the general prescription introduced earlier.
Daniele Oriti: In this construction, we started from this initial part into instead and in law is gravity scale out field that being zero form is democratized on the vertices of the triangulation.
Daniele Oriti: Then of course it propagates over the links.
Daniele Oriti: Which means that your propagator for the scale of field should mostly be located in the if you want to make it propagate on the newer links on the speakerphone complex, you should be Muslim the propagator of the graffiti theory.
Daniele Oriti: So you just have to describe the scale of field and an artist. And then we compose according to the contribution on each floor simplex and the contribution on the URL links or the share that the trailer and then we reconstruct from this the vertex and the propagator of the goofy theory.
Daniele Oriti: This is what is the procedure we adopted. Okay.
Western: Thank you. Welcome.
Daniele Oriti: Okay, one important thing. So of course the coupling scale of field as a physical interest, per se, and it has been useful in in the context of the effective cosmology, as I will discuss later but
Daniele Oriti: There is one important aspect that once you couple the masters care of field to the willful tearing you notice that the way it enters
Daniele Oriti: The action is indeed exactly like a time variable.
Daniele Oriti: So this lends itself to what would be a sort of the parameter ization and the director, the goofy junior level. So in the full of gravity theory, not in in in any classical approximation or any any continuum limit.
Daniele Oriti: Which is simply to take it as if it was a time variable and perform the standard that canonical quantization respite with
Daniele Oriti: You can start from the Lagrangian now define the of the graffiti or a new standard the illusion transformer good when I'm pulling him formalism.
Daniele Oriti: And only click on ties and I are going to have the equal relational time communication relations, not the initial ones that are assumed for the general formalism, and you're going to standard ME, TONY an evolution with respect to this internal clock.
Daniele Oriti: So what your spectrum at the parameter is the theory.
Daniele Oriti: And this was done by add the couple of years ago, and I think it is per se is not the particularly striking development, you could you could expect it. Then we we have been discussing with that for for a while, but I think it lends itself to a number of important developments.
Daniele Oriti: Lost at this foundational level we we asked the question whether there is a quantum statistical mechanics framework underlying goofy theorists.
Daniele Oriti: And notice that this is
Daniele Oriti: Sorry not is it. This is the one of the most interesting and difficult questions you can ask in background independent classical and quantum gravity as Carlos very well.
Daniele Oriti: Even the basic notions of this your mechanics are missing. For example, we asked what is equilibrium in absence of a preferred temporal directions going full quantum gravity.
Daniele Oriti: And there are two main strategies that have been proposed in the literature and that we also apply that to the goofy theory case. One is to use it and entropy maximization principle to define equilibrium states.
Daniele Oriti: And what we did was to the, the, the principle is the following that you define the, the entropy as the log of your state's this petition value the log of your state.
Daniele Oriti: And
Daniele Oriti: You decide to impose a septum constraints, corresponding to fix his petition values for observable, you are interested in, for whatever reason, from the macroscopic perspective.
Daniele Oriti: And the requirement that the entropy is maximize that leads to the gifts form the gifts like form of the states.
Daniele Oriti: So we applied this criteria on to a system of the quantum to trader like a gas. So the three that are using the fog space I introduced the photography to you earlier.
Daniele Oriti: But here, just starting from this definition without having in mind immediately any filter your attic reformulation
Daniele Oriti: So you can using this principle define the partition function corresponding to some set of constraints or fix this petition values for observable so that are called see in the formula ca
Daniele Oriti: And then to make the connection to Guru for curious. Once you have that you simply have to go to a to a basis of the field career sites and then the partition function will take the form of the statistical field theory. So, you will see that the graffiti reaction will be just the revising
Daniele Oriti: Of these constraints in expedition value equation state basis.
Daniele Oriti: So the goofy reaction in codes, whatever constraints you decided to fix microscopically
Daniele Oriti: And interesting choices for this constraints for this relevant variables could be in a ruling us in physical strains that but coming from quantum gravity could be directly them etonian constraint or the physical product.
Daniele Oriti: On the solutions have any time constraint.
Daniele Oriti: And so, in this sense of your pain and grief recovery partition function as a result of the choice of state and maximizing the entropy from a generic system of the quantum data Hydra and you can encode the loop and gravity dynamics in this language.
Daniele Oriti: Then the second
Daniele Oriti: The second type of strategies. One cannot apply to define also equilibrium are the imposition of decay mess conditions.
Daniele Oriti: On the algebra will deliverables for your quantum system. So this, again, is very general. There is a if you have an algebra observable. So then
Daniele Oriti: The existence of a one parameter flow on the algebra.
Daniele Oriti: Basically
Daniele Oriti: Identifies states we satisfy the formula you see on the right hand side of the screen.
Daniele Oriti: For any pair of observable and this fixes again a gifts like form of the quantum state, which then becomes that equilibrium state with respect to the flow that you have seen at it, you have identified at the level of the algebra.
Daniele Oriti: And you can choose flows related to some clock Hamiltonian again in in the context of the parameter ization
Daniele Oriti: Or you can simply are some structural symmetry of your algebra observable and then you choose to study the flow hospital that to those symmetries. Again we applied the same strategy in the concept of the free tier knowing the vile algebra field, the operators.
Daniele Oriti: And then we constructed the equilibrium states that both respite to group type symmetries.
Daniele Oriti: But also the respite to the relational O'clock variable.
Okay.
Daniele Oriti: And then more recently this there was one further development in this statistical mechanics context for a little free theory.
Daniele Oriti: Which is the definition of more Telmo states and the, the development of the so called demo field double formal is meant for the study of term of operations in observable.
Daniele Oriti: And to make a longer story short, the
Daniele Oriti: You can
Daniele Oriti: Define
Daniele Oriti: A corresponding term or representation. So in terms of vacuum corresponding to any given term as gifts state in the fog representation
Daniele Oriti: And again, that's the formula on the top right corner and the two representations are related by a boo boo of transformation in fact quite similar to the ones appearing in the fact of walking effect.
Daniele Oriti: This but will your transformation is not unitary indeed the desert, what you would expect that you will spend a little more representation is equivalent to the fog one
Daniele Oriti: To the initial for one corresponding to zero temperature
Daniele Oriti: And now also in the term of representation. You can be fine condensate or Cohen states.
Daniele Oriti: And then study the term of operations of geometrical observable. So since generic observers in fact the filtering in such a thermal condensate state. And this allows you to compute explicitly the contribution.
Daniele Oriti: Of thermal fluctuations that as to add that up to whatever it is from value you add a zero temperature from that either observable.
Daniele Oriti: And he shine Mady applied this formula is to study term of populations in the context of the goofy theory condensate cosmology, which will will discussing in a while in a few minutes, actually.
Okay.
Daniele Oriti: Now, part three. So these are does developments in the in the format is Miss tension and clarifications or some aspects of the foremost
Daniele Oriti: We have to check if the formula is my for any given model is consistent
Daniele Oriti: Well, the consistency, the quantum level means that you, you want to check out the quantum dynamics is valid for all ranges of the dynamic of variables and is it busy, the statement of randomize ability of the given quantum field theory.
Daniele Oriti: Notice that they're requiring a key model or Akira to be normalized data is to be quantum consistent
Daniele Oriti: Is also a way to
Daniele Oriti: Say control and eliminate quantization and construction and view it so you can have in your model building
Daniele Oriti: And we know several of them in spring for models, the different ways in which you can imposing physical strain, sir, the generalization at the community level that choice of different choices quantization maps. So the quantum annuity quantization and view it is
Daniele Oriti: possible choices of different measure terms. And similarly, in the canonical context that there are quantization ambiguity is in the construction of the Amazonian constraints. Now at the group feature level.
Daniele Oriti: Those become ambiguity definition of your graffiti remodel
Daniele Oriti: But that the test or minimize liability will constrain
Daniele Oriti: Crucially, this type of ambiguity and
Daniele Oriti: Then the other big question is the continuum limit of the full quantum dynamics.
Daniele Oriti: And the first. First of all, we know that the moment we start considering more and more interacting quantum degrees of freedom, we should expect a lot of
Daniele Oriti: Differences, a lot of new physics.
Daniele Oriti: And in general, we would expect different phases and phase transitions relating the different phases as the result of the quantum dynamics. And so this is the general question of what are the phases of us being from all those little quantum gravity.
Daniele Oriti: And
Daniele Oriti: In this context, in the console goofy Curie, the translation of this is
Daniele Oriti: The need to control the non perturbed. But if I'm ization group flow of any given model or classes models.
Daniele Oriti: And notice that evaluating the full partition function. This is the controlling the full continuum limit weightless showing that is well defined means evaluating in food. The lattice gravity path in general and the full screen for model for all complexes
Daniele Oriti: So this becomes the issue of graffiti normalization of turn. But if or non butter butter.
Daniele Oriti: And the general study did that people have followed the is just to treat the Goofy's do is as an ordinary few theories on a on a group manifold. So taking advantage of the group structures for defining a national scale and for setting up the mod integration. So the
Daniele Oriti: Scale for the randomization will flow is them busy indexed by group presentations.
Daniele Oriti: By treating the group as the configuration space.
Daniele Oriti: Now the there are a number of course of technical difficulties.
Daniele Oriti: Respite usual local future is every mostly to do with the convenient or so the final diagrams of the glue factory farm on bargains.
Daniele Oriti: But a larger difficulty, especially in in simply show graffiti remodels which are the most interesting ones from, from our perspective is that we don't really control the theory space is we don't really know what interaction terms are allowed to be generated by the flow.
Daniele Oriti: And, and, for this reason, we haven't multimedia number or results for some crucial models concerning normalization, and most of the work has been done in the 10 serial context when the jury space is well defined.
Daniele Oriti: And under control that, thanks to this to the 10 sorial unitary invariance.
Daniele Oriti: For the one question that is raised in his world present in our mind that whenever we do this work is whether we can immediately give some dramatic interpretation to the flow.
Daniele Oriti: And I don't have a genetic counselor. But my point would be to be my suggestion would be to be very cautious to interpret geometrically in terms of continuing geometry. The, the flow and the type of variables in scales we use
Daniele Oriti: The reason is that the hanging relevant continuum scale at the effective the continuum level.
Daniele Oriti: Will be the result of a combination of the algebraic data like the representations, we use to to index the randomization good flow and the convenient Oryx, as we know from you know geometrical operators into pumping gravity.
Daniele Oriti: So we don't fully control this this limit.
Daniele Oriti: Nor the for the continuing to protection, the geometry interpretation of the flow.
Daniele Oriti: So this is just the picture of a fireman biderman it in. Sorry. Okay, so
Daniele Oriti: And this is just to stress that is from this two points. One is that from from this component or aspects that follow. Most of the technical difficulties of course in fourth dimensional gravity model. So that also algebraic no computational complications.
Daniele Oriti: In addition to the community real ones.
Daniele Oriti: And the other point that I want to emphasize is that
Daniele Oriti: There is a counterpart at the field theoretical graffiti level of the coarse grained steps that are the natural once you want to implement when you study the randomization of spin for models or lattice path in barrels.
Daniele Oriti: Because this cause draining of lattices is exactly what becomes the contraction of divergence of graphs in
Daniele Oriti: The future radical feature level.
In your language.
Daniele Oriti: So just let me just briefly mentioned
Daniele Oriti: The number of results. So as I said, we have a
Daniele Oriti: Say, increasing experience in the calculation of our identity corrections and divergence is in full blown four dimensional simply shall speak for malls in or free theorists, as many of you know, and actually know better than I do.
Daniele Oriti: But so far, that's where we stand. So we were gaining experience. We know some ready to corrections.
Daniele Oriti: But not much more than that. And I will suggest that the key goal of this type of work should actually be more than checking whether a model is divergent or not.
Daniele Oriti: Is should be the amplification of the furious pace. So, really, to characterize can be not already in geometrically the divergent configurations. He potentially divergent configurations
Daniele Oriti: On the other hand, we have a really a lot of experience in Pennsylvania models. And there we have we have started improving the Romans ability of a billion and none of the data models models with or without the local gauging variance and we are when beyond the simple
Daniele Oriti: Models from groups towards models on a homogeneous basis.
Daniele Oriti: And
Daniele Oriti: At the number robotic level.
Daniele Oriti: Again, there is a wide array of the techniques. There is rigorous constructive analysis that shows the existence in a mathematical physics sense of the full path integral that this end up often being physically not very clear, not very explicit
Daniele Oriti: And most of the work instead that is in the context of the
Daniele Oriti: Functional randomization group analysis of the same goofy curious.
Daniele Oriti: And again, in this context, the experience has been built on a number of models in different dimensionality different types of groups compact and non combat.
Daniele Oriti: And Ambien and non a billion.
Daniele Oriti: And with their use simulators.
Daniele Oriti: The
Daniele Oriti: Lessons, we seem to be getting from this experience is that there's a large number of the models that are interestingly, as in totally free or as in totally safe. So there well defined in the food UV from the point of the group. So larger presentations and we have him.
Daniele Oriti: In the opposite direction or that the full flow of the same models.
Daniele Oriti: Will
Daniele Oriti: Identify different places will see different phases, including broken phases of the condensate type. We also learned that you can go beyond the the Milan exactly what seems to be the dominant one in simple density models, thanks to the energy flow.
Daniele Oriti: Okay, now I need to the last part.
Daniele Oriti: And I illustrate a number of directions in which we are trying to extract the continuing physics from roughly two years. So on the first will be very brief. So, one is that
Daniele Oriti: Grew frontier is and tensor models have been studying the as a way to capture the interesting properties of statistical or quantum anybody systems on a random lattice or with random couplings.
Daniele Oriti: Again, this is not my area of expertise or we'll just point you to the literature.
Daniele Oriti: But this is taken and increased
Say,
Daniele Oriti: increasing amount of work in recent years in the last two or three years and it's any another interesting area developments.
Daniele Oriti: And other one is the study of quantum information theoretic properties of graffiti stays and articles now.
Daniele Oriti: Of course it doesn't come as a surprise to any one of you that you know entanglement. He said the very foundations of our new quantum gravity type description of quantum gravity and quantum space. As I mentioned earlier, the very gluing between the data on different
Daniele Oriti: Associated two different vertices has been network is basically the establishing of entanglement between those data.
Daniele Oriti: And even the imposition of gauging violence and each vertex is entanglement between link related the degrees of freedom.
Daniele Oriti: So we know very well that entanglement in our context is directly immediately related to the boat topological so connectivity properties and geometric properties of quantum space.
Daniele Oriti: So in the goofy Curie contexts that you can of course see the counterpart and import all the manual results are that all of us have thing in the for generic for the network's first be natural states and possibly also for spin forms.
Daniele Oriti: Here only mentioned one other type of results which we started exploring recently without discussing it and either because I don't have time.
Daniele Oriti: Is that we know in fact we knew probably before the people doing tensile networks that has been networks are sensor networks.
Daniele Oriti: So it's natural for given Spencer and also be equal, then they become exactly tensile networks as they usually started
Daniele Oriti: Now graffiti restates or generics be natural states.
Daniele Oriti: Are in fact a generalization of tensile networks and, in particular, goofy theory provides a futuristic formulation for random tensile networks.
Daniele Oriti: In which the goofy jury dynamics is a prescription any given model is a prescription for the probability measure for the sensors in the tensile networks.
Daniele Oriti: So this gives the opportunity to study the type of little graphic properties that people have explore for 10 social networks and the way to encode entanglement. Now in a full quantum gravity context, vice versa tensor network techniques could now be used
Daniele Oriti: In in our quantum gravity contest to control it efficiently how entanglement is encoded in our quantum gravity states.
Daniele Oriti: So I just flashed. One thing we did, which is to try to derive the analog some analytical the Utica Yagi formula.
Daniele Oriti: In a full quantum gravity contacts using this goofy theory dynamics as a prescription for random pencil networks and again I'll skip this because I want to move on to other stuff. But we have some results and
Daniele Oriti: We can compute, we can indeed the derive a formula that seems to be the purity convenient Oriel an algebraic analog of the router. Can I again.
Daniele Oriti: Entropy formula, but knowing the dynamical context. So a priori, we could we could compute the quantum dynamical corrections, the quantum gravity corrections to the formula, which would be very interesting.
Daniele Oriti: Okay, I move on to the last
Daniele Oriti: Two points or possibly one
Daniele Oriti: Last the physical context.
Daniele Oriti: So,
Daniele Oriti: We started considering how to extract the cosmological dynamics from the goofy cheery context from the goofy Julie formalism.
Daniele Oriti: Is now a sizable amount of work by various people. The idea being, first of all, that you can interpret quantum gravity condensates graffiti condom space, in particular as continuum homogeneous spaces.
Daniele Oriti: And being condensates they are described by a single collective way function, despite the fact that they encode the infinity of spinetta degrees of freedom.
Daniele Oriti: So this is very convenient. Of course, it's the idea. We have of course grading.
Daniele Oriti: The other basic point is that the idol dynamic equation for such condensates in the simplest approximation already
Daniele Oriti: Can be interpreted as a nonlinear extension of the quantum cosmology equation in particular will loop quantum cosmology equation for structure collectively function for the condensate and you know they pertain it. You don't need to use your the October is being formed expansion.
Daniele Oriti: In fact, you apply directly filter erratic techniques to a struggle immediately the aerodynamic description.
Daniele Oriti: Still, this is running description, as we know from usual quantum many both systems would encode the infinite superposition of firemen diagrams. So all of us being form diagrams in this case.
Daniele Oriti: Your idea being a different position being the cosmology should come out as the aerodynamics of an underlying quantum gravity to. Now, what are the some basis for the two statements I made earlier for the interpretation, we are giving to the States and to the dynamics.
Daniele Oriti: Well, for the states. The simplest condensate state is simply a superposition of
Daniele Oriti: Many body states in which each quantum of the field as the same weight function.
Daniele Oriti: With all the quantum field are at the same way function. And in this simple states of course you're neglecting correlations. So you really need lacking a lot of information about the actual microscopic physics.
Daniele Oriti: So the, the question is whether it's still enough information to rebuild us anything that is meaningful at the continuum geometric level.
Daniele Oriti: And the basis for interpreting the way function as a cosmological we function is that the domain or the way function is in fact
Daniele Oriti: The as a morphic to the mini super space of homogeneous spatial geometries. So now you have a function such a domain. So we exactly typo kinematic a variable of the quantum cosmology function on the media server space of homogeneous spatial geometries.
Daniele Oriti: ID dynamic a level this simple comments they state as an effective dynamics fully capture by the classical equations emotion of the roof will cure.
Daniele Oriti: From the point of your comment says, this would be needed in the infield the CrossFit is aerodynamics and it is no linear equation for such for the wave function sigma labeling the condensate.
Daniele Oriti: So it's formally similar to pump cosmology and the Kingdom article level. But clearly, there's no hubris pay structure for this way function.
Daniele Oriti: Because indeed is a natural dynamic equation. So is no winner.
Daniele Oriti: So for specific more specific cluster models era, like on the lawrenson case but projected to as you to data using the usual
Daniele Oriti: Embedding why map.
Daniele Oriti: And you you coupled with skater field. The along the lines I mentioned earlier by a standing the domain of the field operators and therefore the domain of the condensate way function when additional real variable is being the scale of field variable.
Daniele Oriti: And you do so because just as in quantum cosmology, we want to use of this scale a few variable as a physical book, give us a well defined different by an awful time.
Daniele Oriti: You write down the corresponding action for the model and then you reduce
Daniele Oriti: The
Daniele Oriti: Action and the field to the isotopic type of configurations, meaning the ones, depending on a single spin variables from the microscopic point of view, this will look like considering only equilateral tetrahedron.
Daniele Oriti: The end point here is that you have way functions for the condensate which depends on the real scale on field and a single spin
Daniele Oriti: Obviously the equations emotion simplify enormously. And you can, in fact, write them down.
Daniele Oriti: In like that at the top of the slide.
Daniele Oriti: For with the details of the model encoded in the JD pen and the spin dependent coefficients of the equation, a BMW and the equation is a wonder for simply because we started from a simple model which interactions of the goofy theory field are all the five
Daniele Oriti: Then you approximate this equation, assuming that the interactions are sub dominant as a first approximation, and then you control. What is the effect of the interactions, how the interactions correct to the dynamics.
Daniele Oriti: Then notice that this the casing.
Hello.
Daniele Oriti: Hello.
Muxin Han: This is
Muxin Han: So there's a question. So, so here what you're doing is your first take the action and then reviewing your actions.
Muxin Han: To the symmetry reduce the sector, and then the right person that right
Muxin Han: So, so I'm wondering
Muxin Han: Yeah.
Daniele Oriti: Very well run
Daniele Oriti: The procedure is what is the same. If you do the other way around. So your first ride the equations emotion. Then you reduce them at a special class.
Daniele Oriti: Solutions.
Muxin Han: You got it. So it's called me up its community is to proceed.
Daniele Oriti: As far as I remember, yes.
Ali Parvizi: Okay, okay.
Daniele Oriti: In any case, indeed, we are looking for for a special class of solutions only at first, and then, as I said, here you go for an even special more special regime, which is the one in which the interactions are sub dominant
Daniele Oriti: Now of course this is just the first step. But, but let me point out that
Daniele Oriti: Even though we start the from a model that is motivated by this being famous function, the interactions are certainly there, but they're not expected to be big. In any case, because otherwise the filter by your sponsor will not be valid. With this, you will not trust it.
Daniele Oriti: So you wouldn't really have any reason than to use a specific
Daniele Oriti: Group filtering model motivated by the spring form is punching
Daniele Oriti: Then at this stage we define relational miserables using, as I said, the internal clock variable.
Daniele Oriti: And then simple observable are the volume at given time. The momentum of the scale of field at given time and the energy density of the scale of field it given time. So the typical observable to work with in homogeneous Nigel topic cosmology.
Daniele Oriti: Notice that these are observed was computed in the fundamental Kilburn space, but just assuming that you are in a special state the condensate state.
Daniele Oriti: Now, Q is a concern quantity falling from symmetry of the equations emotion, then you can derive an equation equations emotional for start relating such observer months.
Daniele Oriti: depending also on the
Daniele Oriti: The concert quantities em que that as a formal from symmetries of the equations.
Daniele Oriti: The nice thing one track. First of all, is that when the
Daniele Oriti: Volume basically is largest or in a in a in a classical approximation, your question, sir, approximate the classical Friedman equations if one interprets a particular combination of the coefficients.
Daniele Oriti: In your original models as Newton constant now not is it. This is a sufficient condition is not necessary. You can have something little bit more general. So you can reproduce. Again, the Fremont equation under slightly more general
Daniele Oriti: Restrictions and notice also that the perspective here is that you're basically defining what the Newton constant is looking at the effective continuum dynamics.
Daniele Oriti: What you have at the fundamental level is whatever coupling constant you have in your initial model.
Daniele Oriti: The second gen pointer in this regime in this approximations, is that you see a quantum bounce. So the volume never goes from zero remains positive and it has a single turning point.
Which is, of course, very nice.
Daniele Oriti: And the other nice thing is that if you follow the reviews to
Daniele Oriti: Special case in which only one value for the spin contributes so not only we have just one spin, because we are in the so topic case.
Daniele Oriti: That you assume that the comments which function is none, zero only for one value of the spin, then the equation reuse it. What is basically a little pumpkin cosmology equation.
Daniele Oriti: Which again is quite nice, both from the point of view, pumpkins Marge, I will say, and from the point of view of the graffiti or a cosmology. So we put the two things in touch.
Daniele Oriti: And notice that this casing, which only a single value of the spin dominates is realized then arming clean several contacts, who is not just an arbitrary assumption.
Daniele Oriti: Okay. Now, I mentioned a number of results in refrigerator cosmology and then I guess like closer
Daniele Oriti: So one is indeed the, what is the effect of the interactions. Once you introduce them once you don't neglect them anymore.
Daniele Oriti: Well, people have started the, the, this question only in a very simple case in which you have indeed only one single spin component and one value for the spin
Daniele Oriti: Here at once. You notice that you get an effective graffiti radical dynamic equation for which you can in fact did use an effective dynamics for the volume of the universe.
Daniele Oriti: Which is the formula you see on the lower side lower part of the of the slide. So the coupling constants are the sort of interaction terms you get
Daniele Oriti: Come with powers and prime and double crime and so on and and prime and so on, depending on how many interaction terms you have, and they will give you different powers of the volume in the effective equation.
Daniele Oriti: So there is some room for model building here but nicely. This model building is embedded in the in a more fundamental theory.
Daniele Oriti: In this context, same friends of as to whether there is a way to produce a long lasting acceleration after the bounce. So we know that there is an acceleration of to the bouncer but if you can compute the number of referrals.
Daniele Oriti: Any and it's too small to give anything interesting that without interactions, including interactions.
Daniele Oriti: There is a range of parameters for which, indeed, that you can produce a long lasting accelerated expansion. So something like inflation, but we'll use the directly for quantum gravity.
Daniele Oriti: And what about this seems to be incompatible with a nice classical limit meaning in this range of parameters for this type of interactions you have you get inflation, you get long lasting acceleration, but not a nice exit from inflection.
Daniele Oriti: This is just a very preliminary work in general, there is room for model building in particular, this was for the simplest case in which you only had one spin contributing
Daniele Oriti: Then a number of other results, which I'm not going to discuss in in any any detail at all.
Daniele Oriti: We started considering the role of an isotope is which means relaxing the assumption that the only one spin
Daniele Oriti: Is relevant for the comments every function and for what we've seen so far and I talked with these are nicely tamed late times and they only play a role, close to the quantum bounce, which is what you should expect
Daniele Oriti: And then Marco is shown that the effective cosmological dynamics can be recast in the form of the magnetic gravity, which is interesting in itself.
Daniele Oriti: And this was already shown to be true of course for loop and cosmology dynamics, but here I'm talking about the more general God condensate cosmological dynamics in which you have more than one value for the spin
Daniele Oriti: And then the same effective Friedman equations with bounce and with nice classical behavior and been found. Also on the more general restrictions beyond midfielder and in the relational etonian evolution.
Daniele Oriti: Then we are we have all the ingredients to study cosmological perturbations within the full year.
Daniele Oriti: So we started doing it, although the results are still limited. So let me just mentioned those
Daniele Oriti: In order to have the possibility to study cosmological perturbations, you need to have an ocean of locality of normal generators
Daniele Oriti: And for that, if you want to stay at a different level than nice way to do it is to introduce plots and rods to define a physical, emotional point
Daniele Oriti: So this is what we did when we we generalize the model. I've shown to for free mascara fields.
Daniele Oriti: And then apply the same so topic reduction, we're paying a modified hydrodynamic equation.
Daniele Oriti: And then we assume that we can perturb our condensate around the spatial homogeneous one that satisfies the background equations that I shown in the previous slides.
Daniele Oriti: For this class of states again in the food theory.
Daniele Oriti: We started this, the expectation value of volume fluctuations and try to derive the cosmological power spectrum.
What seems to be
Daniele Oriti: True, is that we find some approximately scaling violence in Europe in a rather than natural manner.
Daniele Oriti: So the dominant part in fact that human genius condensate that will give exact skating balance for the perturbations.
Daniele Oriti: And and we also find it the deviations from these access scale environments are suppressed. As the universe expands. So this is quite nice. And we also find a small relative ambiguity.
Daniele Oriti: Now there is room for excitement, but also for a lot of caution because i mean i i will need the three or four slides that will list all the things we do not understand about this.
Daniele Oriti: Of this and all this. The directions in which you should be improved, but for now let's just say that it's encouraging and in fact we find similar results as far as long wavelength perturbations are concerned, using a different type of approximations in the same
Daniele Oriti: Context that which is a separate universe type approximation.
Daniele Oriti: Okay, then I would have two slides on spherical asymmetrical geometries and black call, sir, but I guess some later. And so we just closed and feel free to ask about black holes and I'll tell you what I know and what I what I don't so far. Thank you.
Jorge Pullin: So questions.
simone: Maybe I can ask her at the beginning I think of section three. Maybe when you were talking about the continually meet
Daniele Oriti: Yeah.
simone: Maybe yes
Daniele Oriti: You tell me if it is the right part
simone: Right here, not that one or quantum consistency perfect design for
simone: So you're shown that there's been a huge amount of work and values explorations in different directions on applying different physical ideas to the setting of goofy theories
simone: But then also, that there are all these possible implications for this painful approach and with the results.
simone: Obtain so far. Where do we stand with respect to like in this ballot least are there things for which we have concrete answers or logos. They come from the results of TT GST or we're still
Daniele Oriti: The only
Daniele Oriti: Results. We have had to do with the quantization ambiguities.
Daniele Oriti: In the sense of, I mean the choice or quantization map.
Daniele Oriti: And this is has to do with the fact that
Daniele Oriti: Okay, so one through your question. In general, the results are limited for what I said. The here, the very beginning. So that so far for the models for which we have a very nice quantum geometric intuition.
Daniele Oriti: The ones that come from spin forms lattice putting together also open to gravity. The only thing we know, and again, you probably know more than I do, is a number of rejected corrections. We know some scaling. We are some scaling results for some digits for some specific models.
Daniele Oriti: Now,
Daniele Oriti: The only thing that this results show so far is that
Daniele Oriti: Quantization I'm you eating I'm you. It is meaning different choice or quantization maps. For example, in the quantization of the same physical strength or similar
Daniele Oriti: Don't do not seem to matter so much because the larger J limit, which is where this divergences appear. And so the flow is really generated
Daniele Oriti: Of the of the models basically wash away this type of differences.
simone: rephrase your answer be seeing
simone: That realization of policy, the current model should be the same as the integration of the parrot crane or BF model. Is that what you're kind of saying or not really
Daniele Oriti: No.
Daniele Oriti: No, because these are really different.
Daniele Oriti: Models. They're not just different.
Daniele Oriti: versions of the same model following from differential quantization map quantization mapper. I have in mind is the, the one that would give a slightly different area spectrum.
Daniele Oriti: For example, because you comprise the flux is differently.
Daniele Oriti: Now this has
Daniele Oriti: Implications for this specific form of the amplitude of the pyramid model.
Daniele Oriti: In fact, I don't think it matters so much for the body cream model, but this differences. These appear in the larger limit.
Daniele Oriti: As you know, so from this point of view, it would seem that different versions of the pyramid model falling from differentials or quantization map, but we behave the same way in the in the movie.
Daniele Oriti: Then of course,
Daniele Oriti: You can you can add different versions of the, of the same model which different also for choices of
Daniele Oriti: Different lower dimensional amateurs. This is a different type of ambiguity, which may or may not be related to the Constitution maps for about this time around we read this. We don't know much, I think.
Daniele Oriti: We also don't know very well, Alabama tries them.
simone: Okay, just one last question. In many of these innovation studies, you seem to include more than just one type of intellectual vertex
simone: And whereas. Usually when we have these like in the superficial definition of the API model we have only one
simone: Is there a lesson from GFP realization that you need more than one or you might still be enough.
simone: To us, what type of cities are
Daniele Oriti: Not a real expert minimization. But as far as I understand from minimization of quantum field theory.
Daniele Oriti: This is a lesson. So the fact that you need more than one of yours is not a lesson from Jeff do meditation is a lesson for my additional quantum field theory.
Daniele Oriti: The point is simply that deliverance is will generate come to terms in general will basically require for consistency new interactions different scales.
Daniele Oriti: That's why I stress that we need to have much better control over the deal is base of the pyramid model or Barack crane or whatever other screen for model we like.
Daniele Oriti: We, what are they allowed interactions, because in general, the flow was which on any of these different directions or different scales.
Daniele Oriti: That's why I was suggesting, not to focus on
Daniele Oriti: How exactly scales even diagram or whether I a certain version of a certain model is finite or not, because that is not so important. What is more important at this stage, I would say, is to control what type of effective interactions are generated
Jorge Pullin: Speaker again.