Recently, I am very interested in Loop Quantum Gravity. But I hope I can know more about the recent development of Loop Quantum Gravity. I mean the development from 2000 to 2011. Any conceptual or practical or technical development in this realm? Further more, I do not know the relationship between Carlo Rovelli's Quantum Gravity and Thomas Thiemann's Modern Canonical Quantum General Relativity. They looks so different. Thank you very much.
There are some links here: https://www.physicsforums.com/showthread.php?p=3597267#post3597267 A recent formulation of the theory is presented here, by Rovelli: http://arxiv.org/abs/1102.3660 Another thing to look at, and see if you can find parts of it you can understand, is a 90-page account of recent spinfoam approach by Livine: http://arxiv.org/abs/1101.5061 On the whole I think it is too hard to be an introduction for beginners, but you should know it is there (and a few parts might be helpful.) There are simpler easier introductions than this, by other people. One for example by Hanno Sahlmann, he is a nice bright young fellow who got his PhD under the direction of Thomas Thiemann. As I recall he uses lots of pictures. I think his presentation is perhaps not so complete and not so hard as the one by Rovelli. Do you know how to use ARXIV.ORG? To find a Sahlmann paper you go to http://arxiv.org and you click on "search" and you type Sahlmann into the author box. It will give you Sahlmann's papers and there will be a recent one called something like "LQG, a short review" There is a Sahlmann VIDEO about "new insights" in LQG. He was asked to give an opening talk at the regular Loops 2011 conference. Google "Loops 2011" and you will get the conference website, and click on "scientific program" and you will see a link to Sahlmann's talk. It might be helpful to watch the video. It reviews very recent work. He is a good clear presenter. There is also a video talk by Rovelli at the same conference. You will see how to click on it if you decide you want to watch. It will be harder and more complete, but might still be helpful. If you have any trouble, ask for help. To save you time here is the link for Sahlmann "LQG, a short review" http://arxiv.org/abs/1001.4188 There are other introductions for beginners, like that, by others of the young people. For example there is this: http://arxiv.org/abs/1007.0402 called Introductory Lectures to LQG, by Dona and Speziale. If Sahlmann is not right for you, and if Rovelli is too hard, then ask again and I or someone else will find other links. My personal opinion is that Sahlmann 1001.4188 is not up-to-date. I would only use something from 2011. But that is partly a personal bias of mine, and you might find his treatment to be just right for you. One has to begin somewhere!
Hi Macus: Do you have any recommendations about Loop Quantum Gravity Ph.D program? There are quite a lot of String/Brane research programs, but Loop Quantum Gravity research programs are rarely heard of. I only know Penn State, and Louisiana State in U.S, Waterloo University in Canada. Is there any more? Thank you very much.
First of all where are you geographically and where do you want to be? I assume your first language is English. They use English at several good LQG centers in continental Europe. Plus there's Nottingham in the UK. Have you thought about grad school in Europe? I'm guessing you are in Usa, and prefer staying in North America. Waterloo in Canada would be great. If you like California there's Steve Carlip's eclectic QG program at UC Davis. He has phd students working in several different QG approaches. I have high respect for him and his approach to the subject. Maybe I shouldn't try to answer in a complete way until I hear more from you. Nottingham (John Barrett) has set up a one-year Masters program which can have a QG focus preparing you for LQG/spinfoam PhD research. The program just started this year, so I have not seen any results. But it seems like a very solid program, good way to get started. Steve Carlip has somebody working in Shape Dynamics (close cousin of LQG) named Henrique Gomes. Gomes coauthors with Tim Koslowski at Perimeter. There is a fair amount of traffic between Perimeter and Davis. Carlip also has a PhD student working specifically in Loop, and I think also someone doing CDT, if I remember right. You already know about the programs at Penn State and at LSU, I gather. there are other smaller programs with just one main person but I won't try to give an exhaustive reply at this point. Still wondering where you are and what you want and why you aren't considering European centers as well.
Great! Then you could start doing some research into what programs are offered and what you need in order to apply to get in. Of course you could simply WRITE to Steve Carlip at UC Davis, and or others and ask what prerequisites they would like to see. It would be educational to learn what they are looking for, and also give you a chance to pick up courses that they think are valuable. But some of that information is probably already online. Have a look at the prerequisites for entering John Barrett's Masters program at Nottingham. The link is in the "introduction to LQG" thread. https://www.physicsforums.com/showthread.php?p=3597267#post3597267 Here is the link for the Quantum Gravity group at Nottingham: http://www.nottingham.ac.uk/mathematics/research/groups/mathematical-physics/quantum-gravity.aspx If you get into the oneyear masters program then I expect a large part of that year will be devoted to a "masters thesis" research paper that is done within the QG group. John Barrett leads that group. He is in contact with the whole LQG community and I imagine the master's program is good practice for succeeding in a PhD program in LQG. My guess is that he would be a good person to place you in a PhD program that is right for you, whether in Europe, the UK, or North America. I can't really help since I don't know you. Depending on where you are, there are people you could go talk with. Jon Engle at Florida Atlantic Jorge Pullin at LSU Steve Carlin at Cal Davis any of numerous great people at Perimeter and at Penn State In fact there is this world map that Francesca created: http://maps.google.com/maps/ms?ie=U...985216139270436.0004843830d27f3e6c50e&t=h&z=0
Regarding conceptual issues have a look at https://www.physicsforums.com/showthread.php?t=544728 https://www.physicsforums.com/showthread.php?t=545596
But the 2010 paper which is the main focus of those threads does not engage what I would call RECENT development of LQG. The recent formulation I told Karmerlo about in post #3 is that in http://arxiv.org/abs/1102.3660 which does not come up in the 2010 paper you cite. The first place I read about the new LQG formulation was in a March 2010 paper "A New Look at LQG". They might have discussed it, but didn't. Just included it in their bibliography as reference [10] and made an inaccurate passing reference on page 44.
Let's not restart the discussion here, but ... ... the recent reformulation does not solve many old issues!
But how do we know that? I have not seen any critical analysis of 1102.3660 which lays out the issues which are not resolved. Except of course the reservations freely stated by the author himself right in the paper. In particular Alex'ov and Roche paper does not seem relevant. I don't believe I have expressed my misgivings about it. It does not even seem honestly objective to me.
Check http://arxiv.org/abs/1111.1879 Discretisations, constraints and diffeomorphisms in quantum gravity Authors: Benjamin Bahr, Rodolfo Gambini, Jorge Pullin (Submitted on 8 Nov 2011) Abstract: In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we review the Consistent Discretizations approach, which is an application of the master constraint program to construct the physical Hilbert space of the canonical theory, as well as the Perfect Actions approach, which aims at finding a path integral measure with the correct symmetry behavior under diffeomorphisms. and Thiemann's papers, of course. There is a research direction focussing on application of the new models; you will not find discussion regarding conceptual issues by looking only at the applications.
Now that is a good paper, I think! An even better up-to-date treatment that highlights some fascinating conceptual problems accessible to researchers is the Freidel et al I was discussing earlier. http://arxiv.org/abs/1110.4833 Continuous formulation of the Loop Quantum Gravity phase space Laurent Freidel, Marc Geiller, Jonathan Ziprick (Submitted on 21 Oct 2011) In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove an isomorphism between the loop gravity discrete phase space and the symplectic reduction of the continuous phase space with respect to a flatness constraint. This gives for the first time a precise relationship between the continuum and holonomy-flux variables... 27 pages I agree! But why would anyone "look only at the applications"? One of the reasons that LQG research is growing and rapidly attracting new people is precisely because it has a lot of accessible research problems---both conceptual and applied.
I think the situation is as follows: there are these 'new models' from which physical predictions can be derived; this atracts a lot of interest and researchers. Then there are conceptualdifficulties wihc are addressed by less people - but which are (at least) equally important. I was in a similar situation when working in a QCD group 20 years ago. QCD was a well establsihed theory, everything was 'standard textbook' - nevertheless there was no convincing idea regardig confinement - and it soon became clear that the well-established quantization failed in the non-perturbative regime. That's why a couple of groups all over the world (Lenz in Erlangen - now Thiemann's chair, Jackiw, O'Rafferty, van Baal, ....) started to develop non-perturbative and canoncal methods. The number of researchers and the list of publications was rather small compared to numerous people wasting time their in three-loop calculations ...
I can see one one could think by analogies. You recall a situation where a few, with vision, worked on the basic theoretical/conceptual problems (in QCD in this case) while there were any who spent a lot of time blindly doing laborious "3-loop calculations" and such like. Different people will of course apply the analogy to the present situation in different ways. For example, I see the Freidel Geiller Ziprick (FGZ) October 2011 paper as a conceptual breakthrough especially when coupled with Bianchi's 2009-2010 reformulation of LQG in terms of a flat manifold with topological defects. These developments involve fundamentally new ways of envisioning quantum geometry. You talk about research that focuses on "applications". I am not sure what you mean by applications. The only active area of application I can think of is to cosmology and other areas where there are potential observations of QG effects. I don't imagine there is a very clear analogy here. I don't minimize the importance of calculating observational consequences that one can look for. The ESA apparently has plans for another CMB mission after the current Planck. The applied calculations are not like laborious 3-loop QCD calculations---not a big investment of man-days. Anyway, the analogies with the present situation are not straightforward, so different people will probably see them differently. BTW the Erlangen group has grown and seems pretty strong to me. I will post some links.
The new models ARE the conceptual breakthroughs which are the fruit of a few people wrestling long and hard with the conceptual issues. The issue of how to think about geometry, in a quantum theory. BTW if you have been paying attention to the new models (the "polytope", the "aharo-bohm", the "zako" to give them nicknames ) you may have noticed the key role played by Bianchi in all three. Now I suppose we will see a growing emphasis at Erlangen on what we can call the "new models." There is an impressive bunch of people being gathered there. The QG group is in two parts, one in Math led by Catherine Meusburger, one in Physics led by Thiemann. I'll get some links. Here is about Meusburger: http://www.algeo.math.uni-erlangen....e/prof-dr-catherine-meusburger/positions.html She recently sent out this email announcement: ==excerpt== A postdoc position will be available in the quantum gravity group within the algebra and geometry group at the Department of Mathematics, University of Erlangen-Nürnberg in Erlangen, Germany... ==endquote== Deadline for application is 15 December. This group is distinct from Thiemann's group. http://www.algeo.math.uni-erlangen....f-dr-catherine-meusburger/research-group.html A postdoc in Meusburger's group is Winston Fairbairn whom you may know of as a Rovelli PhD and co-author. Here is about the quantum gravity group in the Physics Department led by Thiemann: http://theorie3.physik.uni-erlangen.de/people.html This group has grown by the addition of some strong people who have had experience with various "new models" approaches. Maïté Dupuis who comes there from Lyon, for example. She has co-authored a lot with Etera Livine, who was her PhD advisor and also one paper with Freidel. Enrique Borja, who has co-authored with Etera Livine (several) and Freidel (one) Emanuele Alesci, a Rovelli PhD and coauthor. It's also interesting that John Baez' student Derek Wise is there.
To avoid the notoriously difficult Hamiltonian and to provide a tractable formulation from which results (especially in the semiclassical regime) can be derived more easily. The problem is that the underlying conceptual issues are still there but show up in a different (and not so obvious) way. One issue is this: usually the PI (including vertex and measure) is derived via the Hamiltonian; in the new models this derivation is avoided (intentionally b/c the Hamiltonian itself is still poorely understood). The question remains in which way the dynamics of the SF models is related to the original formulation (our understanding is restricted to the kinematical level).
I think this is a fair account as far as it goes, but leaves off the conceptual/aesthetic motivation---which I think is a factor both with Bianchi and with Rovelli. The drive to discover new ways to think the world---new ways to visualize geometry and how it responds to measurement---new quantum concepts of geometry in other words. I mentioned that as I see it the new models we are talking about are aharo-bohm, polytopes, and zakopane. A. The aharo-bohm model is based on topological defects embedded in a flat manifold. The curvature lives on the defects. Rovelli discussed it as a side aspect, possible alternate way to see things, in the zako lectures. It's exciting that Freidel adopts it in the FGZ paper. B. The polytope model (e.g. work by Bianchi) has the nodes of the network be fuzzy indefinite uncertain polyhedra. I find it interesting to imagine space built of such things. Whenever theory has several versions it provides opportunity researchers to learn something by investigating the extent to which they are equivalent or not equivalent. Quantum relativists are growing a new area of imagination. C. A key step in zako model dynamics, according to Rovelli, was presented at conference by Bianchi in January 2010. It has conceptual elegance. The boundary state is a labeled network of measurements, enclosing a labeled foam of process. There is this injective map of SU(2) reps into SL(2,C) reps, which they simply denote by the letter f. This map f contains all the calculation. There is a remarkable mental economy here: All the clutter is removed so that one can readily see what is happening. ======the rest of this post is just notes on sources======== polytope: http://arxiv.org/abs/1009.3402 Pirsa video: http://pirsa.org/10110052/ "Q'tum polyhedra in LQG" polytope-related: http://arxiv.org/abs/1011.5628 aharo-bohm: http://arxiv.org/abs/0907.4388 Google "pirsa bianchi" and you get http://pirsa.org/11090125/ "Loop Gravity as the Dynamics of Topological Defects" aharo-bohm related: http://arxiv.org/abs/1110.4833 (FGZ) zako history: http://arxiv.org/abs/1004.1780 "I emphasize in particular the fact –pointed out by Eugenio Bianchi [2]– that the dynamics of the theory has a very simple and natural definition, largely determined by general physical principles. It is given by a natural immersion of SU(2) representations into SL(2,C) ones. A simple group theoretical construction (Eq. (45) below) appears to code the full Einstein equations.^{2}" Reference [2] is to Bianchi's talk at a January 2010 conference at the Sophia-Antipolis campus. http://wwnpqft.inln.cnrs.fr/previous.html http://wwnpqft.inln.cnrs.fr/pdf/Bianchi.pdf "2 Note added in proofs: For a much simpler and straightforward presentation of the dynamics of the theory, which does not require the full intertwiner space machinery, see [3]." Reference [3] http://arxiv.org/abs/1010.1939 is to a strip-down feynman-rules presentation developed in Moscow, see page 1 of “Simple model for quantum general relativity from loop quantum gravity.”