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Miguel C. Alvarez thesis posted today (Baez student)

  1. Dec 12, 2004 #1

    marcus

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    Miguel C. Alvarez is a PhD student of John Baez at UC Riverside

    he posted his thesis today. congratulations!
    (both to the student and teacher)

    http://arxiv.org/abs/math-ph/0412032
    "Loop Quantization versus Fock Quantization of p-Form Electromagnetism on Static Spacetimes"

    Here's the abstract:

    "As a warmup for studying dynamics and gravitons in loop quantum gravity, Varadarajan showed that Wilson loops give operators on the Fock space for electromagnetism in Minkowski spacetime - but only after regularizing the loops by smearing them with a Gaussian. Unregularized Wilson loops are too singular to give densely defined operators. Here we present a rigorous treatment of unsmeared Wilson loops for vacuum electromagnetism on an arbitrary globally hyperbolic static spacetime. Our Wilson loops are not operators, but "quasioperators": sesquilinear forms on the dense subspace of Fock space spanned by coherent states corresponding to smooth classical solutions..."

    this research can be seen as illustrating the difficulty LQG has in reproducing results in a static flat vacuum---Minkowski spacetime----which are almost taken for granted in that more conventional context. Several people are currently working on this and making gradual progress.

    I cannot judge the thesis itself, but by outward appearances Miguel did not pick an easy problem but, instead, chose an important gnarly issue to tackle for this thesis.

    Miguel has written some for Wikipedia. PF may have already been reading his encyclopedia articles with or without knowing of the author. he also does fencing---which I think is arivero's sport as well

    Thanks to selfAdjoint for pointing out an error in the link as I first typed it. I have corrected it and it seems to be right now.
     
    Last edited: Dec 13, 2004
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  3. Dec 12, 2004 #2

    marcus

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    Here are papers by two other researchers working on getting gravitons in LQG, i.e. approximating a flat vacuum

    http://arxiv.org/gr-qc/0410120
    The graviton vacuum as a distributional state in kinematic Loop Quantum Gravity
    Madhavan Varadarajan
    44 pages
    *
    http://arxiv.org/gr-qc/0409036
    Free vacuum for loop quantum gravity
    Florian Conrady (CPT, Marseille & Potsdam, Max Planck Inst.)
    30 pages, 3 diagrams

    that is 3 papers in one year (in a modest size field)
    so maybe it is becoming something good to work on

    Miguel C-A mentions Varadarajan, I dont know if he cites Conrady or not
     
  4. Dec 12, 2004 #3

    selfAdjoint

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    Marcus the link you give, gr-qc/0412044, is not Carrion-Alvarez's paper. I found the paper here: http://www.arxiv.org/abs/math-ph/0412032
     
    Last edited: Dec 12, 2004
  5. Dec 12, 2004 #4

    selfAdjoint

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    He is trying to quantize the electromagnetic field using Wison Loops in flat Minkowski background. The point is the Wilson Loops; they do not, as is known, correspond to operators in Foch space. But their matrix elements exist when they are linear combinations of "regular coherent states", and these regular coherent states span a dense subset of Foch space.

    Does this strategy sound familiar to you? Recall cylinder functions? A different algebra, but the same strategy!
     
  6. Dec 13, 2004 #5
    Marcus thanks for the link, this paper is really interesting form my and Olias's and Ranyarts perspective!

    Here: https://www.physicsforums.com/showthread.php?t=40814

    I actually used a link by Varadarajan on 'Wik' site to convey a question relative to certain aspects of Fields, dimensionally:http://en.wikipedia.org/wiki/Observable

    Now it seems that the Miguel C. Alvarez thesis paper has some aspects for the Electro-Magnetic-Vacuum theory that I have been banding around on many forums for a long time, of course one can simply state,as admin often do its an unqualified personal theory and warrents a forum ban!

    Again thanks.
     
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