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LQG is not proved to be locally lorentz invariant. (Bee)

  1. Apr 28, 2015 #1

    MTd2

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    Sabine Hossenfelder said...

    Arun: This has never been proved. These deformations are problematic for other reasons, but they don't suffer from the density problem that I alluded to here, if that is what you mean, yes. LQG itself isn't actually based on a space-time network so the argument doesn't apply to it either. The recovery of Lorentz-invariance in LQG though is to my knowledge an unsolved problem. Best,

    B.

    http://backreaction.blogspot.com.br/2015/04/the-problem-with-poincare-invariant.html
     
  2. jcsd
  3. Apr 28, 2015 #2

    atyy

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    I bolded the important point below.

     
  4. Apr 28, 2015 #3

    MTd2

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    The next line The recovery of Lorentz-invariance in LQG though is to my knowledge an unsolved problem. (changed the title)
     
  5. Apr 28, 2015 #4

    marcus

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    Dearly Missed

    http://arxiv.org/abs/1012.1739
    Lorentz covariance of loop quantum gravity
    Carlo Rovelli, Simone Speziale
    (Submitted on 8 Dec 2010)
    The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the "projected" spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.
    6 pages, 1 figure, published in Phys. Rev. D (2011)
    DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1103%2FPhysRevD%252E83%252E104029&v=58853b5b [Broken]

    This paper has been cited 43 times in other research.
    http://inspirehep.net/record/880021?ln=en
    I don't know of anyone finding a mistake in it.
    You might want to look through the list of citations to see if anyone discovered any problems.
    http://inspirehep.net/search?ln=en&p=refersto:recid:880021
     
    Last edited by a moderator: May 7, 2017
  6. Apr 28, 2015 #5

    marcus

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    I don't know how well Bee Hossenfelder knows LQG at this point in her career. She has a lot of interesting opinions on a wide range of subjects but has not written anything related to Loop or Spinfoam QG for quite a while.
    I would suggest asking Wolfgang Wieland about the status of LQG. He is actively exploring the various current formulations and seeing how to relate them to each other, with possible improvements. He calls attention wherever he finds problems.

    I think Wolfgang has cited the Rovelli Speziale paper fairly recently. Maybe he has some comment.
    Here is a reference on page 24 of his paper Hamiltonian Spinfoam Gravity
    http://inspirehep.net/record/1216032?ln=en
    published Classical and Quantum Gravity 31 (2014) 025002
    ==quote page 24==
    To obtain the spinfoam amplitude for the whole discretised space-time manifold we take the product of all Zf over all individual spinfoam faces f and integrate over the free gauge parameters left. These are the edge holonomies gsource and gtarget. We want to ensure local Lorentz invariance [62], and thus take the integration measure to be the Haar measure dg of SL(2,C). This measure is unique up to an overall constant. The resulting quantity matches the EPRL model.
    ==endquote==
    Reference [62] is to the Rovelli Speziale paper.

    Here is an earlier Wieland paper (published 2011) that also refers to it:
    http://arxiv.org/abs/1012.1738
    Complex Ashtekar variables and reality conditions for Holst's action
    Wolfgang Wieland
    (Submitted on 8 Dec 2010 (v1), last revised 24 Jan 2012)
    From the Holst action in terms of complex valued Ashtekar variables additional reality conditions mimicking the linear simplicity constraints of spin foam gravity are found. In quantum theory with the results of You and Rovelli we are able to implement these constraints weakly, that is in the sense of Gupta and Bleuler. The resulting kinematical Hilbert space matches the original one of loop quantum gravity, that is for real valued Ashtekar connection. Our result perfectly fit with recent developments of Rovelli and Speziale concerning Lorentz covariance within spin-foam gravity.
    24 pages, 2 figures. Annales H. Poincaré (2011), 1-24
     
    Last edited: Apr 28, 2015
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