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Refereed publications on Loop/Canonical QG

  1. Jun 18, 2009 #1
    I thought it would be interesting to start a thread organizing a list of **only** refereed publications on Loop/Canonical QG. I suppose this could evolve into a more structured or organized thread? I believe someone asked elsewhere about refereed publications on Loop/Canonical QG. I just include here a very **incomplete** sample of relatively recent papers in peer-reviewed journals to begin with.

    Title: A Lagrangian approach to the Barrett-Crane spin foam model
    Authors: Valentin Bonzom, Etera R. Livine
    Comments: 25 pages, revtex4, 4 figures
    Journal-ref: Phys. Rev. D79: 064034, 2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: Spin-Foam Models and the Physical Scalar Product
    Authors: Emanuele Alesci, Karim Noui, Francesco Sardelli
    Comments: 24 pages
    Journal-ref: Phys.Rev.D78:104009,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: Path integral representation of spin foam models of 4d gravity
    Authors: Florian Conrady, Laurent Freidel (Perimeter Inst. Theor. Phys.)
    Comments: 29 pages, 6 figures
    Journal-ref: Class.Quant.Grav.25:245010,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: Stepping out of Homogeneity in Loop Quantum Cosmology
    Authors: Carlo Rovelli, Francesca Vidotto
    Comments: 16 pages
    Journal-ref: Class.Quant.Grav.25:225024,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: Consistent Loop Quantum Cosmology
    Authors: Martin Bojowald
    Comments: 13 pages
    Journal-ref: Class.Quant.Grav.26:075020,2009
    Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th)
    Title: Comment on "Quantum bounce and cosmic recall" [arXiv:0710.4543]
    Authors: Martin Bojowald
    Comments: 1 page
    Journal-ref: Phys.Rev.Lett.101:209001,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity
    Authors: Martin Bojowald, Golam Mortuza Hossain, Mikhail Kagan, S. Shankaranarayanan
    Comments: 40 pages
    Journal-ref: Phys. Rev. D 79 (2009) 043505
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: Dilaton Gravity, Poisson Sigma Models and Loop Quantum Gravity
    Authors: Martin Bojowald, Juan D. Reyes
    Comments: 31 pages
    Journal-ref: Class.Quant.Grav.26:035018,2009
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: Anomaly freedom in perturbative loop quantum gravity
    Authors: Martin Bojowald, Golam Mortuza Hossain, Mikhail Kagan, S. Shankaranarayanan
    Comments: 54 pages, no figures
    Journal-ref: Phys.Rev.D78:063547,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th)
    Title: Fermions in Loop Quantum Cosmology and the Role of Parity
    Authors: Martin Bojowald, Rupam Das
    Comments: 17 pages
    Journal-ref: Class.Quant.Grav.25:195006,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
    Authors: Martin Bojowald, Tomohiro Harada, Rakesh Tibrewala
    Comments: 56 pages, 42 figures
    Journal-ref: Phys.Rev.D78:064057,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc)
    Title: How quantum is the big bang?
    Authors: Martin Bojowald
    Comments: 4 pages
    Journal-ref: Phys.Rev.Lett.100:221301,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th)
    Title: Recollapsing quantum cosmologies and the question of entropy
    Authors: Martin Bojowald, Reza Tavakol
    Comments: 23 pages, 2 figures
    Journal-ref: Phys.Rev.D78:023515,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th)
    Title: Quantum nature of cosmological bounces
    Authors: Martin Bojowald
    Comments: 26 pages
    Journal-ref: Gen.Rel.Grav.40:2659-2683,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th)
    Title: On the semiclassical limit of 4d spin foam models
    Authors: Florian Conrady, Laurent Freidel (Perimeter Inst. Theor. Phys.)
    Comments: 32 pages, 5 figures
    Journal-ref: Phys.Rev.D78:104023,2008
    Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
  2. jcsd
  3. Jun 18, 2009 #2
    Notice that I have included spin foam models and quantum cosmology.

    That list could include other alternative models as well.
  4. Jun 18, 2009 #3
    As one of the people who asked for recent refereed publications in non-string QG, you have my sincere thanks for compiling this list.

    In particular what I am looking for is a somewhat pedagogical-style review paper, along the lines of the kinds of things that are published in Reviews of Modern Physics, that covers the currently studied formulations of Loop/Canonical QG and establishes their position in the broader context of mainstream physics (i.e. directly addresses the concerns about the long term viability of these theories, directly addressing the issues of Lorentz invariance).

    The list of papers you have provided is definitely impressive, phys rev D and especially phys rev letters are very solid journals. I took a quick glance at several of those but most of them launch right in to particular calculations, nothing wrong with that of course, but I couldn't find the sort of review paper that I was looking for.

    The reason I am looking for such a paper is that if Loop/Canonical QG has become viable, I would consider it part of my general education as a physicist to know about it.

    One specific question I have about the Canonical QG that is being done in these papers, is this the familiar non-renormalizable canonical QG found in most QFT books? If so, is it possible that these papers are working out the cosmological implications of the tree-level diagrams (for which no renormalization is needed) in canonical QG? That would be a worthy task and may lead to observational predictions, but a non-renormalizable theory would be an incomplete description from a theoretical standpoint (of course this is a problem that String Theory is designed to solve).

    My questions in the last paragraph are the kinds of things that I am looking for a Loop/Canonical QG paper to address.
  5. Jun 18, 2009 #4
    Ah, Civilized, that was you, as I now see. And I am Christine, the one you asked about. Nice to meet you. :biggrin:

    Perhaps you may find this following post somehow helpful concerning books and reviews:

    -- List of Books on Quantum Gravity and other helpful tips --

    http://egregium.wordpress.com/2008/01/17/list-of-books-on-quantum-gravity-and-other-helpful-tips/ [Broken]

    And let me know opportunely if they help on the issues you are looking for. Or perhaps you may be willing to open specific threads on those issues, I'm certain there are some experts here that can help.

    Last edited by a moderator: May 4, 2017
  6. Jun 18, 2009 #5
  7. Jun 18, 2009 #6


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    Hello Civil!
    I am not familiar with the term "L/C QG". Most of the LQG community works on non-canonical approach called spin foam. I suppose Christine meant Loop OR Canonical
    Most of the papers which Christine kindly listed are path integral (more exactly sum over histories, spin foam) type---they are not pursuing the canonical approach.

    One still goes back to 1990s canonical to compare and see what carries over. But the shift in focus happened about 10 years ago. And a few people, like Thiemann, still work on the canonical approach.

    A great way to get the whole of LQG research into perspective is to watch the 45 minute invited talk Rovelli gave at the big annual strings conference last year. It is very basic introductory level---you asked for a pedagogical review. And at the end they asked a half dozen questions (and reportedly had more discussion at coffee after.)

    The PDF of his slides is also available so you can get an idea of the outline of the talk.

    I will give the links and also mention what I think are some notable details.
    Last edited: Jun 18, 2009
  8. Jun 18, 2009 #7
    Hi Christine,

    Thanks for all the references, I will have my hands full reading these for a while!

    Hi Marcus,

    Actually I borrowed the term "L/C QG" from the first sentence of the OP in this thread.

    In just a few sentences you answered some of my key questions that will help me get started with this literature. I have access to Rovelli's book so I think I will read that along with some of the papers in this thread.

    Two general questions I am interested in are:

    (1) How do spin foams relate to or generalize quantum fields?

    (2) Is it possible that spin foams will be a complete theory of quantum gravity, or are they intended as an effective field theory that is meant to be a low-energy description, like the standard model? Basically I am asking if there are any known issues that will prevent spin foams from being a complete description (which would be fine for me, I'm in condensed matter theorist so I see nothing wrong with a tractable model that is only valid in some range).

    I welcome answers from anyone. I'm reasonable so I don't expect anyone to post detailed answers, hopefully just links to papers (preferably refereed) where the questions are addressed. Not that detailed posts would be a bad thing, since as a long-term resource this sub-forum seems like a high-profile starting point for people who know some physics and are curious about spin foams /LQG.
    Last edited: Jun 18, 2009
  9. Jun 18, 2009 #8


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    I'm glad to hear that! In that case I should really stress the Rovelli talk video and the slides PDF. Here are the links:

    There is no truly no better introduction. It is concise. (Also more up-to-date than the book since the book is essentially 2003 and the Strings talk was 2008.) And it directly addresses the questions you are asking.

    Your question (1) is addressed directly in the first 2 or 3 slides. For LQG in general, not specifically the spin foam formalism.
    Your question (2) is implicitly addressed throughout the talk. That is the aim. To have a theory, not just an effective theory. So far no permanent obstacles have been identified that would prevent LQG from achieving that goal.
  10. Jun 18, 2009 #9


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    In response to the general line of questions from Civil, the most didactic thing that I can recall Rovelli saying recently (most suitable for fresh arrival newcomers) is from a 3-way seminar talk (Ashtekar-Rovelli-Freidel) where he gave the second 20-minute talk out of three, held May 5, 2009. The whole hour talk plus slides PDF is here:

    Rovelli lists 5 questions which he then says are ill-posed (not the right questions).

    ==quote Rovelli's slides, text only, no diagram sketches==
    ...Some questions
    1. Is quantum space made out of loops and spin-networks or tetrahedra and 4-simplices?
    2. Is flat space formed by ...
    Claim: these questions are ill posed.

    1. Is quantum space made out of loops and spin-networks or tetrahedra and 4-simplices?

    The meaningful question in quantum theory is not how something is, but how it responds to a measurement.

    There is no space “between” quanta of space, and it makes no sense to ask what is the geometry between one quantum and another, or inside a quantum, or what is the “geometry of quantum”. It is like asking for the “shape of a photon”. Or “What do I measure if I measure the energy in the space occupied by half a photon?”

    2. Is flat space formed by few tetrahedra with high spin, or by many tetrahedra (or loops) with low spin?
    [That is as pointless as asking:]How many particles are there in the Fock vacuum?
    How many particles are invoved in a two-particle interaction?

    Quantum theory gives the probability for measurement outcomes: it does not describe “what is between measurements”.

    “In between pictures” are just descriptions of the ways I decide to do calculations. They are different for different measurements, and at different orders in perturbation theory.

    From this perspective (I dont know if you can accept it or not) it is possible to have a UV-finite complete theory that is predictive given a finite number of experimentally determined parameters and yet does not say 'what is really there' at planck scale. It might not be LQG, LQG is a possibility but no one can say how probable (most theories fail and are replaced). If it is LQG in whatever version, whatever formalism, then it is still naive to say that space IS a spin network----a spin network is a quantum state of spatial geometry (a basis element for a certain hilbertspace) that allows certain calculations of geometric observables and you can define matter fields on top of it (instead of say a piece of Minkowski space). And it is naive to say that spacetime IS a spin foam---a spinfoam is a history of spatial geometries that gives a way to calculate transition amplitudes by a kind of path integral method. You could say that a spinfoam represents spacetime as a trajectory of geometries from some initial to some final state of geometry. But one isn't saying that either space or spacetime is made of some kind of stuff. The idea is that all the other fields---matter etc.---live on the gravitational field (which is geometry) and so one needs a mathematical representation of the state of geometry for other fields to life on (as extra quantum numbers labeling the nodes and links of the graph) so one has to have a barebones minimal state geometry that can support this other stuff.
    Something that is not located in space but serves as a minimal location for the rest.

    So what the LQG have been focused on is calculating with a new spinfoam model invented or discovered in 2007. Calculating the graviton propagator where the model is constrained to be approximately flat. This is where the most interesting papers would be (2008-2009) I think. Also in the subfield about black holes. Rovelli and Krasnov have a recent paper about the black hole in full LQG (instead of in a symmetry reduced model used earlier.)

    Perhaps I'm responding to quickly without giving enough thought, or saying too much detail. Perhaps I'll give it another try tomorrow.
    Last edited: Jun 18, 2009
  11. Jun 18, 2009 #10
    Thanks again! I read the 40 slides from Strings 08, but haven't watched the video yet. This is a great set of slides, it very clearly lays out the main points of interest.

    So far I think I understand that LQG is an attempt to express spacetime as a quantized SU(2) gauge theory that is also invariant under diffeomorphisms. In particular, the Wilson loops (spin networks) can be reparametrized under diffeomorphisms, and UV divergences are avoided because the reparametrizability of the spin networks means that the theory is not at all sensitive to short distance scales at all.

    I would say that on first reading the foundations of the theory seem very deep, mostly because the full implications of local diffeomorphism invariance seem mind-boggling. Clearly a lot of things follow from this constraint, including local Lorentz covariance, which becomes almost trivial compared to the full diffeomorphism group.

    Specific questions:

    (1) In slide 10 we have spins j on the links and intertwiners i on the nodes. Am I correct to infer that spins are elements of SU(2) and intertwiners are elements of some diffeomorphism group?

    (2) Is it correct to infer that the group of diffeomorphisms is diff(U) where the manifold U is a four dimensional open ball?

    (3 resolved myself, see next post) Does anyone know of a reference where wilson loops are used as the basis of states for an SU(N) gauge theory? I know them only as gauge invariant observables, do not know how to think of them as states.

    (4) It seems like diffeomorphism invariant QFTs are a subset of Homeomorphism invariant QFTS i.e. Witten's Topological Quantum Field Theories. Is this similarity superficial only, or are there references that discuss the fundamental principles of LQG from a TQFT point of view?
    Last edited: Jun 18, 2009
  12. Jun 18, 2009 #11
    I just read the may 5th notes, and I agree with you that Rovelli's comments about ill-posed questions was good for a newcomer to see. For me these notes also helped to seperate the big ideas of the theory from the various calculational approximation techniques that have been / are being tried.

    I'm trying to see the reasoning of Friedel's statement:

    "The basic postulate of Loop Quantum gravity is the statement that
    SU(2) spin networks states form a complete basis of the kinematical Hilbert space of pure gravity."

    This almost makes sense to me, does this have something to do with SO(3,1) or SL(2,C), but were do they get SU(2).

    I think I have answered my own question (3) in my previous post, my revised understanding the spin networks are just generalized wilson loops that have spin valued indices at the nodes and links, the Wilson loop observables I am used to are expectation values of that loop integrated over all gauge fields, now I see that the loop is analogous to the spin network, that is the spin network is somethings which can be integrated over all configurations of the metric to find a gauge invariant observable.

    I accept it to such a high degree that I am greatly relieved to see CR making such statements, the emphasis on observables and calculations over mental pictures is, IMHO, the mark of a mature quantum physicist.

    I'll look into this, but just in terms of providing bearing or context in a massive field of literature, in what sense is this spinfoam model new, and how much does it depart from what was done before?
    Last edited: Jun 18, 2009
  13. Jun 19, 2009 #12


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    In 2006 people in Rovelli's group were calculating the graviton propagator using the old Barrett-Crane spinfoam (vertex amplitude formula), and they were trying to recover Newton's law behavior, something falling off as the square. Wrong behavior was found and a paper immediately appeared. I forget who by. So then there was a race to find an improved amplitude formula, mostly in early 2007, mostly between Freidel-Krasnov and on the other hand
    Rovelli-Engle-Pereira and some others. Etera Livine was instrumental. I think he showed that the FK and the REP were equivalent in the case of a certain ("immirzi") parameter being less than one, which is the case that matters. I'm recalling from memory.

    It's hard for me to say how much does it depart. Superficially it doesn't look like much of a change, a slightly different formula giving different amplitude numbers, but in terms of results the effects have been quite remarkable. Suddenly spinfoam fits very well with the kinematic canonical results. It has a place for the immirzi parameter (important in the canonical approach), it reproduces the area and volume operators' spectra.

    Getting a fit has additional significance for the researchers themselves (I think) because canonical Lqg is in certain way unfinished. It describes quantum states of geometry but boggles at their evolution: the dynamics.

    So what Rovelli does in the Strings 2008 talk is he presents the what could be called the kinematics with spin networks and when it is time to move on to the dynamics he says "now you can forget everything I said up till now and I'm going to give you a completely different development of LQG" which is with spinfoams. This may sound like an unsatisfactory state of affairs, but he was presenting Lqg to some 400 string theorists at Cern and this is how he chose to do it, so it's probably the best way to look at it at least for now.

    A spinfoam is so to speak a picture of a spin network evolving in time. The links of the static network become polygons. So instead of a graph there is a 2-complex.

    Rovelli and his postdocs still seem to think with spin networks but calculate almost always using spinfoam and a related formalism called group-field-theory. I would say the prevailing attitude is that it is all one theory LQG whatever formalism is being used, canonical or path integral. As a spectator I just give my impressions and don't speak with any authority.
    Last edited: Jun 19, 2009
  14. Jun 19, 2009 #13
    Sorry for the title of this thread; actually I thought about "non-string" instead of "Loop/Canonical", but I didn't want to sound that I was excluding string theory in a negative way. Yet I believe that "Loop/Canonical", although having a precise meaning in QG, have ended up being the general term for "quantum general relativity", that's why I used it here. Anyway, this thread was just a suggestion: to organize peer-refereed papers in "quantum general relativity" (or the best equivalent term for it), not just arxiv submissions.

    And as I mentioned in my original post and in #2, I included other than the strictly "Loop/Canonical" approaches, like, eg, spin foam models.

    Hope this clarifies.

    I suspect the title of the thread cannot be changed?
    Last edited: Jun 19, 2009
  15. Jun 19, 2009 #14
    For "completeness", some refereed papers on the canonical approach (mostly by Thiemann et al):

    Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
    Authors: Benjamin Bahr, Thomas Thiemann
    Comments: 60 pages, 8 figures
    Journal-ref: Class.Quant.Grav.26:045012,2009
    Title: Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
    Authors: Benjamin Bahr, Thomas Thiemann
    Comments: 36 pages
    Journal-ref: Class.Quant.Grav.26:045011,2009
    Title: Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
    Authors: Bianca Dittrich, Thomas Thiemann
    Comments: 12 pages
    Journal-ref: J.Math.Phys.50:012503,2009
    arXiv:hep-th/0608210 [ps, pdf, other]
    Title: Loop Quantum Gravity: An Inside View
    Authors: Thomas Thiemann
    Comments: 58 pages, no figures
    Journal-ref: Lect.NotesPhys.721:185-263,2007
    Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
    Authors: K. Giesel, T. Thiemann
    Journal-ref: Class.Quant.Grav.24:2565-2588,2007
    Title: Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
    Authors: K. Giesel, T. Thiemann
    Journal-ref: Class.Quant.Grav.24:2499-2564,2007
    Title: Algebraic Quantum Gravity (AQG) I. Conceptual Setup
    Authors: K. Giesel, T. Thiemann
    Journal-ref: Class.Quant.Grav.24:2465-2498,2007
  16. Jun 19, 2009 #15
    Just wanted to add this paper that was mentioned in another thread:

    Title: Loop quantum gravity: an outside view
    Author: Hermann Nicolai, Kasper Peeters, Marija Zamaklar
    Journal-ref: Class.Quant.Grav.22:R193,2005

    This is exactly the sort of refereed review paper which is targeted at people with a background in high-energy physics but not in LQG that I was asking for. It is a few years old, but otherwise it looks ideal.

    Thanks all, and in the light of this morning I see that my posts seeking a general LQG education were not so well placed in this thread, so in the future I will start a new thread if I have those sorts of questions.
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