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What is the recent development of Loop Quantum Gravity 
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#73
Feb2112, 03:19 PM

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PF Gold
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Since the topic of polyhedra has come up, I'll mention some recent work in that area:
http://arxiv.org/abs/1009.3402 (google "bianchi polyhedra") Polyhedra in loop quantum gravity Eugenio Bianchi, Pietro Dona', Simone Speziale 32 pages As it happens, I see that Eugenio Bianchi is at UC Berkeley this week giving a couple of talks. He has a coauthor in the physics department so maybe they are working on something. Anyway there is this paper about quantum polyhedra. A quantum polyhedron (state space a space of intertwiners) can be thought of as a blur of possible classic polyhedra. Volume may be specified, also number of sides and areas. But shapes of sides may be indeterminate. A quantum state of geometry might be imagined as a collection of quantum polyhedra, with adjacency relations. You aren't guaranteed the ability to match the faces. The loop literature does not say something naive like space IS a bunch of quantum polyhedra, that is just one way to think about the theory. There are various ways of approaching and visualizing that give intuition. Use them if they help you but don't get hung up on them. Another way, also worked out primarily by Eugenio, is to think of it as a quantum theory of topological defects. All the geometry, the curvature etc, is concentrated on the cracks and crevasses between chunks, which are flat (everything is flat except at the defects where they meet.) This also is a way to visualize LQG, a guantum theory of the defects between otherwise flat chunks of space. The Freidel Geiller Ziprick paper takes off from Bianchi's work on this and, as you probably recall, develops it further. http://arxiv.org/abs/0907.4388 (google "bianchi aharonov") Loop Quantum Gravity a la AharonovBohm Eugenio Bianchi 19 pages 


#74
Feb2212, 04:19 AM

P: 74

Hi Marcus, hi Tom,
my original goal of the last post was to say thank you for the good discussion. But to meet the goal of this thread, here are some general remarks or better my motivation: Also for me the basic requirement is a clear testable version of QG that reproduces classical geometry (where applicable) and resolves the cosmo singularity. (like you Marcus) But more must be possible: an explainantion of dark matter / energy and inflation. Currently, LQG is one of the best candidates to meet all these criteria. So, from the QG point of view I'm rather a 'LQG follower'. But that don't prevent me from a critique of some aspects of the current research, like Tom does. I never start my own QG program. I started with the investigaton of 4dimensional smooth manifolds to understand general aspects of dynamics. Currently there is a lot of work to find the Hamiltonian via trial and error (my opinion). So I miss a general concept for the next steps. The large number of workers on that field is a great advantage. My own philosophy is a little bit different: I agree to produce a testable version reproducing known theories in some limits. Since 20 years ago I learn in my first topology lecture at the university of the existence of exotic R^4. So immediatly I wa interested. What is the relevance of exotic smoothness for physics? The first results came from Carl Brans (I met him in 1995). Then we are both occupied with the book project. The idea was very simple: two referenece systems (or systems of charts, i.e. an atlas) are equivalent if both a diffeomorphic to each other. But then two nonequivalent reference systems (representing different physics) are nondiffeomorphic. In 4 dimensions it can be indepedent of the topology. Therefore exotic spacetimes can be seen as different physical systems (of a spacetime with fixed topology). My own investigations began around 1995 (when I thought to have studied enough differential topology) but with classical relativity theory by showing that exotic smoothness can be the source of a gravitational field. Nearly 10 years later we found the first relation to quantum mechanics by constructing a factor II_1 von Neumann algebra (the Fock space of a fermion). You maybe remember on the discussion in 2005 in this forum. There are only very few people working in this field. A student of M. Marcolli, Christopher Duston, joined our community and began to calculate the Euclidean path integral for different exotic smoothness structures. It was folklore that exotic smoothness contributes (or better dominates) the path integral but no one showed it. Chris was the first to tackle this problem by perturbatively calculate it. His results inspired me to calculate also the Lorentz case. In two papers we calculate (nonperturbatively) the exotic smothness part to show area quantization as a result (confirming LQG). In parallel we try to find another description of exotic R^4's (without infinite handlebodies) and end with an amazing relation to codiemnsion1 foliations. This relation brought us back to think about QG. The space of leafs of a foliation was one of the first examples of a noncommutative space and geometry by Connes. In case of our foliation we obatin a factor III_1 von Neumann algebra also known as observablen algebra of a QFT (in the algebraic sense). Currently we also find relations to ConnesKreimer renormalization theory and to the Tree QFT of Rivasseau (arXiv:0807.4122). But enough about history, my real motivation for this work is the relation between geometry and physics. Especially the question, what is quantum geometry? The simple answer, the quantization of the spacetime, is not correct. (I will have a lookinto Bianchis polytop theory soon.) So from the philosophical point of view, I'm interested in the relation between geometry and quantum theory, especially which one is the primary principle. Because of exotic smoothness, I believe it is geometry. But then I have to understand the measurement process etc also from a geoemtrical point view. Another driving force is the naturalness, i.e. to derive the expressions for the Dirac action, the standard model etc. from geometrical expressions. This brings me back to your discussion here. I miss the guiding principle in the current constructions in LQG. Of course there are excepts (Freidel is one, sometimes Rovelli). Everyone speaks about unification but currently there are alwyas two entities: the spin network and the dynamical spacetime (or the string and the background). A real unification should end with one entity. But now to your interesting questions: what is the fundamental structure of (L)QG: 1) PL or smooth manifolds with diffeomorphisms factored away  resuting in triangulations? 2) generic spin networks? As I tell in my previous post, I'm impressed by Marcollis topspin model. Then the spin network (as 1dimensional complex) produces the 3manifold as branched cover. Then we have one entity (the network) producing the space. The spin network (as the expression of holonomies) has a topological interpretation: every closed loop in the network must be corespond to one element of the fundamental group of the 3manifold. After the solution of Poincare conjecture we know that the fundamental group characterizes a 3manifold uniquely. Therefore (in my opinion) the two cases 1) and 2) are more connected then anybody thought. The second question: in (L)QG, do we have to use a 3dim. or a 4dim manifold to start with? is much harder to comment. Usually one starts with a globally hyperbolic 4manifold (SxR, S Cauchy surface) and one has to discuss only the topology of the Cauchy surface. Otherwise later one speaks about fluctuating geometries (by quantum fluctuations) which can be result in a topology change (at the Planck level). But a topology change destroys the global hyperbolicity (now naked singularities appear). So, at first one has to discuss the global hyperbolicity condition. Even in the exotic smoothness case one lost this condition (see http://arxiv.org/abs/1201.6070). But did we really need it? The main reason for its introduction were causility question. But now we know (after some work of Dowker about causal continuity) that topology change is possible. Naked singularities seem bad at the first view but we need them (to prevent the horror of Parmenides block universe, i.e. a complete determinism). Such a singularity separates the past from the future. Then we cannot completely determine the trajectory of a particle That is for me a necessary condition to implement quantum mechanics. Therefore for my opinion, one should start with a spacetime (4dim) and should look for codim 1 subspaces (the 3dim space). 


#75
Feb2412, 03:35 PM

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PF Gold
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Thanks Torsten, this is one of the most thoughtful and interesting posts in my experience here at the BTSM forum! I appreciate your care in laying out your thoughts on QG and different smooth structures.
I just heard a 90 minute presentation at the UC physics department by Eugenio Bianchi which had some suggestive parallels with your research focus. He was talking about the dynamics of topological defects (as an alternative formulation of Loop gravity.) There were questions and discussion during and after so it took the full two hours. Steve Carlip participated quite a lot. Good talk. The slides overlapped some with those in the PIRSA video which you can watch if you wish: Google "pirsa bianchi" and get http://pirsa.org/11090125/ PIRSA:11090125 Loop Gravity as the Dynamics of Topological Defects Speaker(s): Eugenio Bianchi Abstract: A charged particle can detect the presence of a magnetic field confined into a solenoid. The strength of the effect depends only on the phase shift experienced by the particle's wave function, as dictated by the Wilson loop of the Maxwell connection around the solenoid. In this seminar I'll show that Loop Gravity has a structure analogous to the one relevant in the AharonovBohm effect described above: it is a quantum theory of connections with curvature vanishing everywhere, except on a 1d network of topological defects. Loop states measure the flux of the gravitational magnetic field through a defect line. A feature of this reformulation is that the space of states of Loop Gravity can be derived from an ordinary QFT quantization of a classical diffeomorphisminvariant theory defined on a manifold. I'll discuss the role quantum geometry operators play in this picture, and the perspective of formulating the Spin Foam dynamics as the local interaction of topological defects. Date: 21/09/2011 As I say, many of the slides are the same as those of today's talk, but there seem to be new results, and I got more out of it the second timeeither today's presentation contained more intuition and insight or else the questions by Carlip and Littlejohn helped bring out stuff. Anyway great! I can't help suspecting that there is some kinship between the dynamics of topological defects and your investigation of differential structures. One obvious difference from the September PIRSA talk was that this came after the October Freidel Geiller Ziprick paper in effect laying out a "constrain first then quantize" approach, developing the "Loop Classical Gravity" concept. There were several references to FGZ http://arxiv.org/abs/1110.4833 . 


#76
Feb2512, 03:40 PM

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PF Gold
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Looking over the schedule of the April meeting of the American Physical Society, one sees that there will be an invited talk reviewing current research in Spinfoam and Loop QG
http://meetings.aps.org/Meeting/APR12/Event/170161 Eugenio Bianchi (Perimeter Institute) Loop Quantum Gravity, Spin Foams, and gravitons Loop Quantum Gravity provides a candidate description for the quantum degrees of freedom of gravity at the Planck scale. In this talk, I review recent progress in formulating its covariant dynamics in terms of Spin Foams. In particular, I discuss the main assumptions behind this approach, its relation with classical General Relativity, and its lowenergy description in terms of an effective quantum field theory of gravitons. The session of invited QG talks is chaired by Jorge Pullin, who also chairs the regular session "Quantum Aspects of Gravitation" http://meetings.aps.org/Meeting/APR1...EventID=172413 Here are a few of the talks scheduled for the regular QG session. http://meetings.aps.org/Meeting/APR12/Event/170104 Hal Haggard (UC Berkeley) Volume dynamics and quantum gravity Polyhedral grains of space can be given a dynamical structure. In recent work it was shown that BohrSommerfeld quantization of the volume of a tetrahedral grain of space results in a spectrum in excellent agreement with loop gravity. Here we present preliminary investigations of the volume of a 5faced convex polyhedron. We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume. In particular, we are interested in discovering whether the evolution generated by this volume is chaotic or integrable which has important consequences for loop gravity: If the classical volume generates a chaotic flow then the corresponding quantum spectrum will generically be nondegenerate and the volume eigenvalue continues to act as a good label for spin network states. On the other hand, if the volume flow is classically integrable then the degeneracy of the corresponding quantum spectrum will have to be lifted by another observable. We report on progress distinguishing these two cases. Either of these outcomes will impact the direction of future research into volume operators in quantum gravity. http://meetings.aps.org/Meeting/APR12/Event/170098 Rodolfo Gambini, Nestor Alvarez, Jorge Pullin (Montevideo, LSU) A local Hamiltonian for spherically symmetric gravity coupled to a scalar field Using Ashtekar's new variables we present a gauge fixing that achieves the longstanding goal of making gravity coupled to a scalar field in spherical symmetry endowed with a local Hamiltonian. It opens the possibility of direct quantization for a system that can accommodate black hole evaporation. The gauge fixing can be applied to other systems as well. [my comment: related paper= http://arxiv.org/abs/1111.4962 ] http://meetings.aps.org/Meeting/APR12/Event/170100 Jacopo DiazPolo, Aurelien Barrau, Thomas Cailleteau, Xiangyu Cao, Julien Grain (LSU, CRNS Paris) Probing loop quantum gravity with evaporating black holes Our goal is to show that the observation of evaporating black holes should allow the standard Hawking behavior to be distinguished from Loop Quantum Gravity (LQG) expectations. We present a Monte Carlo simulation of the evaporation of microscopic black holes in LQG and perform statistical tests that discriminate between competing models. We conclude that the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal specific quantum gravity footprints. [my comment: related paper= http://arxiv.org/abs/1109.4239 ] http://meetings.aps.org/Meeting/APR12/Event/170102 Seth Major (Hamilton College) Coherent States and Quantum Geometry Phenomenology The combinatorics of quantum geometry can raise the effective scale of the spatial geometry granularity predicted loop quantum gravity. However the sharply peaked properties of states built from SU(2) coherent states challenge the idea that such a combinatorial lever arm might lift the scale of spatial discreteness to an observationally accessible scale. For instance, the LivineSpeziale semicoherent states exhibit no such lever arm. In this talk I discuss how an operational point of view suggests a different class of coherent states that are not built from states with microscopic classical geometry. These states are introduced, compared to previous coherent states, and the status of the combinatoric lever arm is discussed. 


#77
Feb2612, 05:22 PM

P: 74

Thanks a lot for your words, Marcus
As usual, I like your recommendations. So I will have a look into Bianchi's article. The lecture is really interesting. It seems we share the same passion... Maybe one thought which is independent of exotic smoothness: In our article about topological Dbranes http://arxiv.org/abs/1105.1557 we discussed wild embeddings to use it as a quantum version of D branes. An embedding is a map i:N>M so that i(N) is homeomorphic to N. The embedding is called tame if i(N) is represented by a finite polyhedron. Examples are Alexanders horned sphere or Antoines necklace. One of the main characteristica of a wild embedding is that the complement M\i(N) is mostly a nonsimple connected space. Other examples of wild embeddings are also called fractals... In section 5.3 we describe a wild embedding by using Connes noncommutative geometry, i.e. we associate a C* algebra to the wild embedding. All the resulst of this paper seem to imply that a quantum version of a D brane is a wild embedded Dbrane. Maybe also any other quantum geometry is of this kind. But now I will study your recommendations.... 


#78
Feb2712, 01:13 AM

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torsten, I strongly believe that you miss one important point regarding your own work; it seems to me that (once you succeed with your program ;) you will be able to explain why we live in a fourdim. spacetime!



#79
Feb2712, 01:43 AM

P: 74

Good point Tom, that was one of the reasons I began to study exotic smoothness. When I heard from this result, I studied superstring theory. But then I changed to differential topology to understand this result.



#80
Feb2812, 01:51 AM

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Yes good point: the multitude of structures does make D=4 special, or is one of the things that makes it special. Another thing to note is the suggestion of spontaneous dimensional reduction at extremely small scale which has appeared in several separate theory contexts as reviewed by Steve Carlip. BTW I forgot to mention another invited Loop talk at the April APS meeting.
There is a session called Advances in Quantum Gravity consisting of three invited talks. One of the these, already mentioned, is by Eugenio Bianchi: a review of recent advances in Loop QG Spin Foams and gravitons. Abstract: http://meetings.aps.org/Meeting/APR12/Event/170161 I overlooked another Loop invited talk to be given by Ivan Agullo from Penn State: http://meetings.aps.org/Meeting/APR12/Event/170160 Beyond the standard inflationary paradigm The inflationary paradigm provides a compelling argument to account for the origin of the cosmic inhomogeneities that we observe in the CMB and galaxy distribution. In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises, and a clarification of what the transPlanckian problems are and what they are not. In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles employed here. I hope to find something on arxiv that can give more of an idea what this will be about. I could not find anything the first try. It's late, have to look further tomorrow. =======EDIT====== Well, I looked again this morning and couldn't find anything on arxiv that I could recognize as a clear indication of what this talk might be about. Ivan Agullo has worked a lot with Leonard Parker. He was at Parker's institution and is now with Ashtekar group at Penn State, I think. He brings a lot of nonLoop cosmology to Loop, or so it seems to me. I woujld like to see a paper coauthored by Agullo and Ashtekar, but I can't find one so far. I will check ILQGS for a talk by Agullo. Inflation is important because a some previous approaches to inflation bring on the multiverse ailment. You invent an inflaton field and then spend the rest of your life trying to make excuses for it. 


#81
Feb2812, 01:19 PM

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Ah hah! I found a March 2011 ILQGS talk by Agullo
http://relativity.phys.lsu.edu/ilqgs/agullo032911.pdf Observational signatures in LQC He refers to work in progress by Ashtekar, William Nelson, and himself. This is precisely what is apparently not yet written up so I can't find on arxiv. It would be the basis of his invited presentation at the American Physical Society April meeting in Atlanta: http://meetings.aps.org/Meeting/APR12/Event/170160 Beyond the standard inflationary paradigm Ivan Agullo (Penn State) ... In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises... In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles... BTW today (28 February) the ILQGS will have a talk by Marc Geiller, one of the coauthors of the FGZ paper. This paper topped our fourth quarter MIP poll last year. It offers a new approach to constructing LQG as a "quantization" of a classical theory. Google "ILQGS" and get http://relativity.phys.lsu.edu/ilqgs/ Scroll down to March 2011 to get links to audio and slides of Agullo's talk. Geiller's talk about the FGZ research is currently at the top of the same page: http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf Continuous formulation of the loop quantum gravity phase space He's at "ParisDiderot": the Diderot campus of the University of Paris, on the right bank near the city's southeast edge. 


#82
Feb2812, 07:08 PM

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Tomorrow 29 February the Perimeter QG group has talk by Wolfgang Wieland
which I hope will be online as video and slides. Postdocs at PI get to bring visitors to the Institute. I think Wolfgang is coming as Eugene Bianchi's guest. His homebase at this point is Marseille. http://pirsa.org/12020129 Spinor Quantisation for Complex Ashtekar Variables Wolfgang Wieland Abstract: During the last couple of years Dupuis, Freidel, Livine, Speziale and Tambornino developed a twistorial formulation for loop quantum gravity. Constructed from AshtekarBarbero variables, the formalism is restricted to SU(2) gauge transformations. In this talk, I perform the generalisation to the full Lorentzian case, that is the group SL(2,C). The phase space of SL(2,C) (i.e. complex or selfdual) Ashtekar variables on a spinnetwork graph is decomposed in terms of twistorial variables. To every link there are two twistorsone to each boundary pointattached. The formalism provides a clean derivation of the solution space of the reality conditions of loop quantum gravity. Key features of the EPRL spinfoam model are perfectly recovered. If there is still time, I'll sketch my current project concerning a twistorial path integral for spinfoam gravity as well. 29/02/2012  4:00 pm Wieland's 29 February talk (available online at ILQGS) will evidently be based on this paper: http://arxiv.org/abs/1107.5002 Twistorial phase space for complex Ashtekar variables Wolfgang M. Wieland (Submitted on 25 Jul 2011, last revised 24 Jan 2012) We generalise the SU(2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group SL(2,C). We show that the phase space for complex valued Ashtekar variables on a spinnetwork graph can be decomposed in terms of twistorial variables. To every link there are two twistorsone to each boundary pointattached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum gravity. Key properties of the EPRL spinfoam model are perfectly recovered. 18 pages, Classical and Quantum Gravity 29 (2012) 045007 


#83
Feb2912, 02:44 AM

P: 74

Thanks marcus for your effort.
Yes inflation is indeed important. But one of the current problems is the infinity of the inflation process, i.e. if the inflation process (with the inflaton) is started then there is no known process which stops the inflation. The second problem is agin the naturalness: there ar ean infinity of possibilities for the potential of the inflaton field. Here we made also progress with exotic smoothness at the beginning of the year. http://arxiv.org/abs/1201.3787 An exotic S^3xR can be partly described by a cobordism between the 3sphere and a homology 3sphere (Poincare sphere for instance) and vice versa. Except for the Poincare sphere, all other homology 3spheres are negatively curved (I mean at least one component of the curvature tensor is negatively curved), a corrolary of Perelmans work. Therefore we get the change: postive curvature > negative curvature > positive curvature For this case we explicitely solve the Friedman equations including the dust matter (p=0) and obtain inflation (I mean an exponential increase) which stops. Also one word about the interesting claims of Carlip. It is an amazing fact from general manifold theory that the simple 2disk is one of the important tools. (I recommend a proceeding article of Michael Freedman "Working and playing wit the 2disk") Therefore the dominance of 2dimensional objects around the Planck scale was not amazing for me (I remember Loll et.al. got also this result in CDT). 


#84
Feb2912, 06:44 PM

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Wonderful video talk by Wolfgang Wieland!
http://pirsa.org/12020129/ Goes back to the original complex Ashtekar variables and goes forward to the new double spinor version of Loop developed by Dupuis, Freidel, Livine, Speziale, Tambornino... Maïte Dupuis is currently a visitor at Perimeter, there seems to be a convergence of people interested in this "twistorial" or dual spinor version of Loop. I've been watching Wieland's lecture and was quite impressed. See what you think. Torsten, you are pointing out suggestive parallels with the differential topology approach you have in progress. It would certainly be remarkable if there proved to be a solid bridge. At first it seemed very strange to be going back to the original complex version of the Ashtekar variables. But he makes it look like a convincing move, and somehow the immirzi parameter reappears as a real number, which I would never have expected! 


#85
Mar112, 01:26 PM

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It's clear that there are some shifts going on. Generational, geographical, and even (on a minor level) formal.
Loop is fast moving. It isn't easy to keep in one's sights. The "target" that one is trying to describe and follow is evolving rapidly. Generationally, we have to watch more carefully some younger representatives of the mainstream Loop. Wolfgang Wieland, Eugenio Bianchi, Maite Dupuis, Simone Speziale, Etera Livine... (not a complete list.) Also we should notice firsttime faculty positions, some in comparatively new places, for people who were only recently postdocs: Engle made faculty at Florida Atlantic Sahlmann, Giesel and Meusberger made faculty at Erlangen Singh faculty at LSU Dittrich faculty at Perimeter Bianchi, Haggard, Agullo are giving talks at the April APS in Atlanta. These are comparatively young researchers. Two of the talks are invited. These are not the only Loop talks at the APS meetingI just mention these three because of the generational angle. There seems to be some increased activity at UC Berkeley. Bianchi was just here and gave two talks. In the formalism department, you could say that the "paradigm" of Loop is shifting towards what Dupuis, Speziale, Tambornino describe in their January 2012 paper Spinors and Twistors in Loop gravity and Spin Foams For me, the paper which best characterizes the new Loop wave is Wieland's Twistorial phase space for complex Ashtekar variables together with his PIRSA talk of 29 February. I have now viewed the whole 80 minutes, including the questons and discussion and I think it is a "must watch". Geographically, there seems to be a shift from Europe to North America. Part of this is that Perimeter is so strong. It grabs many of the creative young people and if it does not get them on a longer term basis then it brings them there for one month visits to collaborate with people there already. For instance: Maite Dupuis, Marc Geiller and Wolfgang Wieland are all three currently visiting. There is some kind of critical mass effect. The next biannual Loops conference, Loops 2013, will be at Perimeter. Plus another factor is that the Usa has some catching up to do in Loop, which means faculty openings and growth at the newer centers south of the border. Here's an informal window to help follow geographical movement: http://sites.google.com/site/grqcrumourmill/ Sample postdoc moves in 2012: Ed WilsonEwing/ Marseille > LSU Marc Geiller/ Paris > Penn State Thomas Cailleteau/ Grenoble > Penn State Philipp Höhn/ Utrecht > Perimeter Faculty: Hanno Sahlmann/ Pohang > Erlangen Renate Loll/ Utrecht > Nijmegen Note that three of the postdoc moves are in the general direction Europe>Usa 


#86
Mar212, 11:51 AM

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Earlier I was trying to find a write up that would preview the content of Agullo's invited talk at the April meeting of the American Physical Society. The best source, I now realize, is this set of ILQGS slides by William Nelson:
http://relativity.phys.lsu.edu/ilqgs/nelson101811.pdf and the corresponding audio http://relativity.phys.lsu.edu/ilqgs/nelson101811.wav or http://relativity.phys.lsu.edu/ilqgs/nelson101811.aif William Nelson's talk is a "musthear". It's some very good work (as Lee Smolin comments at the end) and is going to change how we view cosmology. It is joint work by Agullo, Ashteker, Nelson, and it just happens that Nelson gave the ILQGS presentation and Agullo will present it at the April APS in Atlanta. ILQGS also has an interesting blog where various presentations are discussed by OTHER researchers, who often give more basic intuitive explanations of what the talk is about. Brizuela (AEI) comments on Nelson's talk, Julian Barbour (!) comments on Tim Koslowski's talk about shape dynamics, Frank Hellmann (AEI) on Jacek Puchta's about an extenstion of Spinfoam... Check out the blog, pedagogically it complements the seminar talks and makes them more accessible. http://ilqgs.blogspot.com/ Some future talks listed here: http://relativity.phys.lsu.edu/ilqgs/schedulesp12.html Note DiazPolo upcoming talk on Loop BH evaporation (there's a relevance to obs. testing): http://arxiv.org/abs/1109.4239 


#87
Mar412, 07:20 PM

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Something I've heard a lot in talks recently is "the Loop hypothesis".
It gives a useful perspective for understanding what the various QG formulations called Loop have in common. It is the hypothesis that you can TRUNCATE the dynamic geometry of GR to finite degrees of freedom and then recover the continuous for all practical purposes. The Loop truncation is to consider making geometric measurements at only a FINITE SET OF POINTS. So you naturally get a graph of places where you measured some volumes and some face areas between adjacent chunk volumes. The details of what constitute possible geometric measurements are not importantangles and lengths are also allowed. What matters is the observer can only make a finite number of measurements, and that defines the state. I'm thinking that's what science is about: The aim of quantitative science is to explain what we can observe and to predict thereabout . And we never get to make more than a finite number of observations. So a state of nature (nature's geometry) is naturally going to be truncated to a finite set of points with adjacency relations and whatever labels. The Loop hypothesis is that this is sufficient to explain and predict what we can observe. It's minimalist. The hypothesis (a kind of gamble) is that this will prove to be sufficient to recover the continuous classical picture by taking more and more points (more elaborate networks of observation). 


#88
Mar412, 07:34 PM

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I think there are two different truncations.
In Rovelli's Zakopane, he talks about a truncation which is a good approximation. The FGZ idea is that the full space can be split into nice parts and the continuum recovered exactly (not just for all practical purposes) by joining them together. The idea is that is one can do that, one just needs to quantize each part separately. 


#89
Mar512, 12:43 PM

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PF Gold
P: 23,228

For me, what FGZ does is one further step in the process that goes back to the 1990s of finding the most mathematically convenient way to implement the Loop hypothesis*truncating geometry to a finite number of degrees of freedom, truncating to N degrees of freedom and then letting N→∞. There are several, many, ways this has been tried. It is all the same quest. You may wish to focus on just two initiatives: Zakopane and FGZ. But I do not wish to restrict my view that way. Remember the LewandAsht measure, the holonomyflux algebra, the LewandOkolSahlThiemann theorem? I see it as all part of the same journey. I suppose that history could replace the Zako formulation and keep some features of it. I particularly like the Hilbertspace of squareintegrable functions defined on a cartesian product of G where the Lie Group G can refer to either the rotations or the full Lorentz. And I like the gamma map from SU(2) reps to SL(2,C) reps. I hope those features are kept, but who can say? Suppose the group G becomes somehow twistorial? It would still be like Zako, square integrable functions on G^{E=#edges} in a way, but it would also be different. Or suppose the hilbertspace of functions on the group manifold become not complexvalued but somethingelse valued? I really liked Wolfgang Wieland's pirsa talk. It gave me a glimpse of where the further evolution of this "loop hypothesis" could go. Maybe neither Zako or FQZ is final or exactly right. It would be a shock if it were The important thing is to have something simple definite and clearmathematically welldefinedat each step along the way. Zako served as that last year and perhaps also this year. We have to keep our eyes open for what will take shape by spring of 2013, when another Loops conference is coming due. *I was just listening to Marc Geiller talk about the FGZ work: http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf http://relativity.phys.lsu.edu/ilqgs/geiller022812.wav He calls it the "Loop assumption" instead of the Loop hypothesis, and he says concretely what he means on slide #8 early in the talk. I have the impression now that I hear many people using this idea, which has entered the shared vocabulary of the Loop community. Perhaps it was always one of the shared concepts but I didn't notice it until recently. 


#90
Mar512, 02:03 PM

Sci Advisor
P: 8,631

So are FGZ talking about what Rovelli calls the graph expansion, which he distinguishes from the vertex expansion? http://arxiv.org/abs/1102.3660 (p19).



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