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The Immirzi parameter

  1. Jul 29, 2015 #1
    https://en.wikipedia.org/wiki/Immirzi_parameter
    Quote:The Immirzi parameter seems to be the only free parameter of vacuum LQG

    Hence LQG should provide formulas (or numerical calculation) for all dimensionless parameters of standard model . For now, at least the raw idea, where they come from.

    How LQC solves the naturalness problem? Why gravity is so weak, or, saying it more correctly, why particles are so lightweight (in comparison with Planks mass)? Where this tiny fraction originates?
     
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  3. Jul 29, 2015 #2

    fzero

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    LQG proposes to provide a quantum description of gravity. It does not claim to "unify" gravity with the other forces. There have been papers proposing how fermions and the rest of particle physics might be incorporated, but this is not the main goal of the research program. Your questions are not within the domain of mainstream LQG.
     
  4. Jul 30, 2015 #3
    Interesting. I was thinking LQG is a candidate for TOE, but apparently it is not.
    Whats about string theory?
     
  5. Jul 30, 2015 #4

    Demystifier

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    Unlike string theory, LQG was never a candidate for TOE.
     
  6. Jul 30, 2015 #5
    Thank you.
    And how String theory manages to make these big (or tiny) numbers just of pi, e, 2, 3, exp() and ln()?
     
  7. Jul 30, 2015 #6

    fzero

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    String theory suggests how to do so, but an explicit solution where we get Standard Model physics, a small cosmological constant, and a realistic mass spectrum has not been found. In fact it can be very difficult to extract Standard Model parameters from string theory if the string coupling is not small in the low-energy regime. I think most of the relevant issues would be covered in this recent review: http://arxiv.org/abs/1204.5296
     
  8. Jul 30, 2015 #7
  9. Jul 31, 2015 #8

    Demystifier

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  10. Jul 31, 2015 #9

    marcus

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    Or a quantum description of geometry-cum-gravity. It's a fair description. The textbooks and review articles by people currently active in the field make this clear. I don't recall anyone saying the main goal was unification.

    The other topic of this thread seems to be the Immirzi parameter. Here's a recent paper. E. Livine is one of the longtime leaders in Loop QG--it could be worthwhile taking a look at his reflections on this still somewhat mysterious parameter.

    http://arxiv.org/abs/1507.00851
    Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a Cut-off for Quantum Gravity
    Christoph Charles, Etera R. Livine
    (Submitted on 3 Jul 2015)
    8 pages
    ==sample quote from introduction, pages 1 and 2==
    ...At a more effective level, it enters the loop quantum gravity dynamics in a non-trivial way and seems to be a crucial parameter in the description of quantum black holes (see the review [6]). It also appears to control the couplings to fermionic field and possible quantum gravity induced CP violation [7–10]. ...

    Here, we would like to underline the crucial difference between the role of the Immirzi parameter at the classical level and in the quantum theory. Classically, it appears as a coupling constant in the Holst-Palatini action for the first order formulation of general relativity [3]. In the effective field theory paradigm, one can then investigate its renormalisation flow, together with the Newton’s gravity constant and the cosmological constant, as proposed in [18, 19]. In the full quantum theory, it appears as a more essential parameter defining directly the fundamental quanta of geometry---scaling the discrete spectra of the area and volume operators---in Planck units. We would like to trace back, in the loop quantization procedure, where the Immirzi parameter acquires this deeper role.

    We will use the very simple example of the holonomies of the Ashtekar-Barbero connection on a space-like 3- hyperboloid embedded in flat space-time and look at its dependence on both the hyperboloid curvature and the Immirzi parameter...
    ...
    ...
    This compactification, which can be understood as the origin of the discrete spectra for areas and volumes, [has the effect] ...that the choice of observables in loop quantum gravity for a fixed Immirzi parameter does not allow to distinguish all points of the classical phase space. In that sense, the Immirzi parameter quits being a mere coupling constant but appears to play the new effective role of a cut-off, similarly to the energy scale cut-off in usual quantum field theory. This is consistent with the view that it determines the size of discrete quanta of geometry and points towards the perpective that the bare theory would in the “continuum limit” β → 0. Then specific physical situations will require specific values of the Immirzi pa- rameter, which will determine the suitable truncation of the effective corrections to general relativity (resulting from loop quantum gravity) to use in that case. ...
    ==endquote==
     
    Last edited: Jul 31, 2015
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