Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gambini QG thread

  1. Oct 31, 2004 #1

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    We should probably have a QG thread focused on the work of the Uruguayan physicist Rodolfo Gambini and his co-workers, such as Jorge Pullin (LSU) and Rafael Porto (Carnegie-Mellon) and others.

    I will get some links. I would like to understand better how Gambic QQ fits together with more familiar types of Loop QG as done by Ashtekar, Rovelli, Smolin, Thiemann, Bojowald ....

    We are lucky at PF because someone (a grad student i think) in contact with Gambini group has visited PF and written us some posts. But we have to develop our own base of knowledge because grad students normally have only limited time for message boards.

    the first thing I notice may seem superficial to some people, but I think it is significant: someone on the team is a better than average writer. If you grab a Gambini, Pullin, et al paper out of archiv, chances are it will be more than average clear and concise.

    another thing is that Michael Reisenberger, whose most recent 3 or 4 papers were co-authored with Rovelli, is currently in Uruguay----and also
    note that Gambini most recent paper is
    Consistent discretizations and loop quantum geometry
    which says explicitly that it is building a bridge between the CD approach and LQG.

    So IMHO we should look at the CD approach and see what is special, what it offers, and how it have some common ground and might fit together. As a watcher (not a participant) I think one should check this out.

    Maybe some time Rovelli and Gambini will find something in common and write a joint paper, who knows?

    As a side comment, Ashtekar's most recent paper (Gravity and the Quantum) mentioned Gambini-group's hamiltonian as an alternative to Thiemann's hamiltonian. this was at the top of page 20.
    ----quote Ashtekar---
    A key open problem in loop quantum gravity is to show that the scalar/Hamiltonian constraint---either Thiemann’s or an alternative such as the one of Gambini and Pullin---admits a 'sufficient number' of semi-classical states. Progress on this problem has been slow because the general issue of semi-classical limits is itself difficult in any background independent approach (12). However, a systematic understanding has now begun to emerge and is providing the ‘infrastructure’ needed to analyze the key problem mentioned above [38, 52].
    ---end quote---

    Well actually Gambini and Pullin are proposing more than just an alternative to the various LQG hamiltonian constraints, they have a way of avoiding the constraint equation. they introduce a very-small-step unitary evolution operator. I hesitate to call this "time"-evolution. because time is such a loaded word that the minute (:smile:) one says it one is swept away in a tide of confusions. but for better or worse they got rid of the damned hamiltonian constraint and they have this very-small-step discrete evolution operator which maybe will turn out to be legitimate (!) who knows?

    Personally I like zig-zags in the development of physical theory because of the comedy and unexpectedness. The Gambini-group line of research has the potential to add a surprise element and make the story more interesting. So I want to learn more about this.
     
  2. jcsd
  3. Oct 31, 2004 #2

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

  4. Oct 31, 2004 #3

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    If anyone else is exploring the Gambic QG approach, along with me, I can facilitate by supplying links to their earlier papers corresponding to the footnote references.

    I am looking at two most recent papers and working backwards to the work cited there. For example near the beginning of "Canonical QG and CD" they say:
    ---quote gr-qc/0408025---
    The new proposal we have put forward (http://arxiv.org/gr-qc/0206055 ), called consistent discretization is that, in order to make the discrete equations consistent, the lapse and the shift need to be considered as some of the variables to be solved for. Then one has 16 equations and 16 unknowns. This might appear surprising since our intuition from the continuum is that the lapse and the shift are freely specifiable. But we need to acknowledge that the discrete theory is a different theory, which may approximate the continuum theory in some circumstances, but nevertheless is different and may have important differences even at the conceptual level. This is true of any discretization proposal, not only ours.

    We have constructed a canonical approach for theories discretized in the consistent scheme (http://arxiv.org/gr-qc/0205123 ). The basic idea is that one does not construct a Legendre transform and a Hamiltonian starting from the discretized Lagrangian picture. The reason for this is that the Hamiltonian is a generator of infinitesimal time evolutions, and in a discrete theory, there is no concept of infinitesimal. What plays the role of a Hamiltonian is a canonical transformation that implements the finite time evolution from discrete instant n to n +1. The canonical transformation is generated by the Lagrangian viewed as a type I canonical transformation generating functional. The theory is then quantized by implementing the canonical transformation as a unitary evolution operator. A discussion of an extension of the Dirac procedure to these kinds of systems can be seen in (http://arxiv.org/gr-qc/0405131 ).
    ---end quote---

    So those are their footnotes translated into links, to facilitate getting the article cited. here then is a short list of Gambini-group CD papers

    CD and Loop Quantum Geometry
    http://arxiv.org/gr-qc/0409057

    two titles: Canonical QG and CD----alternatively CD and QG
    http://arxiv.org/gr-qc/0408025

    Canonical quantization of general relativity in discrete space-times
    http://arxiv.org/gr-qc/0206055

    Canonical quantization of constrained theories on discrete space-time lattices
    http://arxiv.org/gr-qc/0205123

    Dirac-like approach for consistent discretizations of classical constrained theories
    http://arxiv.org/gr-qc/0405131
     
    Last edited: Oct 31, 2004
  5. Oct 31, 2004 #4

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    It is becoming clear that Gambini group is in full swing of activity and is very prolific of papers just now. I went back to the "Time in QG" thread and got Edgar's list
    I will just add it here and try to sort things out, eliminating possible repetitions, later.
    Wait. first this must be a treasure:
    K. Kuchar “Time and interpretations of quantum gravity” in “Proceedings of the 4th Canadian conference on general relativity and relativistic astrophysics”, G. Kunstatter, D. Vincent, J. Williams (editors), World Scientific, Singapore (1992), online at http://www.phys.lsu.edu/faculty/pullin/kvk.pdf
    I do not know this paper but this must be important for anyone interested in time and QG.

    Now here is the list that Edgar1813 just gave us:
    http://arxiv.org/gr-qc/0302064
    Consistent discrete gravity solution of the problem of time: a model
    Authors: Rodolfo Gambini, Rafael A. Porto and Jorge Pullin
    *
    http://arxiv.org/quant-ph/0209044
    A physical distinction between a covariant and non covariant reduction process in relativistic quantum theories
    Authors: Rodolfo Gambini, Rafael A. Porto
    New J.Phys. 5 (2003) 105
    *
    http://arxiv.org/quant-ph/0205027
    Relational Description of the Measurement Process in Quantum Field Theory
    Authors: Rodolfo Gambini, Rafael A. Porto
    New J.Phys. 4 (2002) 58
    *
    http://arxiv.org/quant-ph/0105146
    Relational Reality in Relativistic Quantum Mechanics
    Authors: Rodolfo Gambini, Rafael A. Porto
    Phys.Lett. A294 (2002) 129-133
    *
    http://arxiv.org/gr-qc/0101057
    Relational time in generally covariant quantum systems: four models
    Authors: Rodolfo Gambini, Rafael A. Porto
    Phys.Rev. D63 (2001) 105014
    *

    And here are an additional one from another Edgar1813 post:

    A relational solution to the problem of time in quantum mechanics and quantum gravity: a fundamental mechanism for quantum decoherence
    http://xxx.lanl.gov/abs/gr-qc/0402118

    ============
    Here are some others, which I supplied (and may be duplicates, so that I will have to eliminate them when I sort things out)

    Gambini Porto Pullin
    Realistic clocks, universal decoherence and the black hole information paradox
    http://arxiv.org/abs/hep-th/0406260

    Gambini Porto Pullin
    No black hole information puzzle in a relational universe
    http://arxiv.org/hep-th/0405183

    R. Gambini, S. Jay Olson, J. Pullin: Unified model of loop quantum gravity and matter
    http://arxiv.org/gr-qc/0409045

    Rodolfo Gambini, Rafael Porto, Jorge Pullin: Fundamental decoherence from relational time in discrete quantum gravity: Galilean covariance
    http://arxiv.org/gr-qc/0408050
     
    Last edited: Oct 31, 2004
  6. Oct 31, 2004 #5
    Marcus I have presented many links to Pullin-Gambini for some time(sorry pun not intended!),these of course have been under different handles/user-names, I can honestly state that some of the papers have been the reason I have been banned from PF(currently awaiting my 5th banning ;), these papers are as you state very intruiging and thought provoking.

    But I have a number of problems with one or two papers, the first is from some time ago, although my stubborness in my intuitive thinking on Entropic States may be the underlaying problem?..but anyway a recent paper:hep-th0406260, confirms my belief in an underlaying problem, and it basically deals with an 'Ideal' reference paramiter for information, information that is for any given system.

    Just to give an idea, what is the 'maximum' amount of information needed in order to give a correct value in Time-Measuring devices, what is the accepted reliable local and far off location true..mean?
     
  7. Oct 31, 2004 #6

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Dear Handwave, I was sorry to learn of your many bannings! Right now, my problem in this thread is to get things sorted out so that I can narrow it down to perhaps some 4 or 5, or halfdozen, papers that are all one needs to print out if one wants to learn the basics about this new proposal of Consistent Discretization. I would like to find the minimal spanning set of papers that approximately covers the subject---hopefully not too technical but including some nittygritty.
     
  8. Oct 31, 2004 #7

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    snapshot of Gambini
    http://cgpg.gravity.psu.edu/online/Html/Seminars/Fall1998/Gambini/

    another, at the May 2004 Marseille conference
    http://perimeterinstitute.ca/images/marseille/marseille010.JPG

    so far the paper about consistent discretizations that seems most accessible to me is what I believe was the first one:
    http://arxiv.org/abs/gr-qc/0206055
    Canonical quantization of general relativity in discrete space-times

    Abhay Ashtekar gave some perspective on the Gambini-group approaches in his most recent survey paper: "Gravity and the Quantum"
    on page 29 he is talking about the 4 main ways being explored to include dynamics in the theory. Two of the four are Gambini ideas:
    1.Thiemann master constraint
    2. Gambini et al knot invariants
    3. spinfoam---various people
    4. Gambini et al. CD

    ---quote page 29 Ashtekar---
    ...In simple examples, this procedure leads to physically viable quantum theories. In the gravitational case, however, the procedure does not seem to remove any of the ambiguities. Rather, its principal strength lies in its potential to complete the last step, iii), in quantum dynamics: finding the physically appropriate scalar product on physical states. The general philosophy is similar to that advocated by John Klauder over the years in his approach to quantum gravity based on coherent states [36].

    A second strategy to solve the quantum scalar constraint is due to Gambini, Pullin and their collaborators. It builds on their extensive work on the interplay between quantum gravity and knot theory [27]. The more recent developments use the relatively new invariants of intersecting knots discovered by Vassiliev. This is a novel approach which furthermore has a potential of enhancing the relation between topological field theories and quantum gravity. As our knowledge of invariants of intersecting knots deepens, this approach is likely to provide increasingly significant insights. In particular, it has the potential of leading to a formulation of quantum gravity which does not refer even to a background manifold (see footnote 9).

    The third approach comes from spin-foam models [35,39], mentioned in section II C, which provide a path integral approach to quantum gravity. Transition amplitudes from path integrals can be used to restrict the choice of the scalar constraint operator in the canonical theory. This is a promising direction and Friedel, Noui, Perez, Rovelli and others are already carrying out detailed analysis of restrictions, especially in 2+1 dimensions.

    In the fourth approach, also due to Gambini and Pullin, one first constructs consistent discrete theories at the classical level and then quantizes them [42]. In this program, there are no constraints; they are solved classically to find lapse and shift fields. This strategy has already been applied successfully to gauge theories and certain cosmological models. An added bonus here is that one can revive a certain proposal made by Page and Wootters to address the difficult issues of interpretation of quantum mechanics which become especially acute in quantum cosmology, and more generally in the absence of a background physical geometry...
    ---end quote---

    reference [42] is to a paper we have been reading at PF, namely
    Gambini/Pullin
    Consistent Discretizations and Quantum Gravity
    http://arxiv.org/gr-qc/0408025
     
    Last edited: Nov 1, 2004
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?