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Mass Gap, Solved?

  1. Mar 24, 2010 #1

    MathematicalPhysicist

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    If I am not mistaken the problem of the mass gap in in QYM, is a claymath problem, if the author of the next blog has proven it, shouldn't his article make more background noise, i.e be noticed by the media?

    Here's the link:
    http://marcofrasca.wordpress.com/?s=mass+gap

    Or he hasn't proven his theorem, math-wise.
     
  2. jcsd
  3. Mar 24, 2010 #2
    I think he is saying that he has a proof in the strong coupling limit with evidence from lattice calculations that the underlying idea is valid for finite couplings. That would be nice but still some way short of solving the mass gap problem.
     
  4. Mar 24, 2010 #3
    Marco Frasca had an argument with Peter Woit at the latter's blog regarding exactly Yang Mills theory:

    http://www.math.columbia.edu/~woit/wordpress/?p=1657

    I think the discussion started at the wiki entry.

    If his work is correct maybe he can finally edit that article. :)
     
  5. Apr 19, 2010 #4
    The question went this way. I have got a paper published on Physics Letters B

    http://arxiv.org/abs/0709.2042" [Broken]

    where I stated some theorems producing as a final result the infrared gluon propagator. This propagator displays a spectrum of excitations with a massive ground state. This result relies on a theorem that I claimed to have been proved that maps a massless quartic scalar theory on a Yang-Mills theory. I stated that these theories have common classical solutions that can be used to obtain a quantum field theory describing an identical behavior for both. QFT for the scalar theory was published, authored by me, in Physical Review D

    http://arxiv.org/abs/hep-th/0511068" [Broken]

    The proof of the mapping theorem was declared wrong by Terry Tao, the Fields medalist, with an intervention on the discussion in the Wiki entry of Yang-Mills theory (see http://en.wikipedia.org/wiki/Talk:Yang–Mills_theory" [Broken] in the section "Removed "Integrable solutions of classical Yang-Mills equations and QFT"). After this criticism I have written to Terry asking for clarifications. Indeed, he removed the corresponding entries in his site Dispersive Wiki claiming the proof was incorrect. He asked to me to get a correct proof to be published in an archival journal. I obtained this last year in Modern Physics Letters A

    http://arxiv.org/abs/0903.2357" [Broken]

    Terry recognized, in a private communication and removing the entry to my paper in http://tosio.math.toronto.edu/wiki/index.php/Talk:Yang-Mills_equations" (just click on FraE2007 in Terry's removal comment and see also follow-up), that my new proof was indeed correct but that these common solutions between the scalar field theory and the Yang-Mills theory hold, in the more general case, only perturbatively in the strong coupling limit: Mapping exists perturbatively. But note that this is all I need to get my proof completed!

    Meantime, a proof on the lattice that the mapping theorem holds also in d=2+1 was obtained by Rafael Frigori and published on Nuclear Physics B

    http://arxiv.org/abs/0912.2871" [Broken]

    see also

    http://marcofrasca.wordpress.com/2009/12/16/mapping-is-confirmed-by-lattice-computations/" [Broken].

    So now, the proof is both correct and complete thanks also to the pivotal intervention of Terry Tao that helped me to fix it by pointing out a flaw in the original demonstration. But until Terry will not ask to me to restate the original material, improved as I said, I will not do that.

    Currently, I am working out QCD phenomenology using this low-energy limit of Yang-Mills theory that makes all computations manageable. Indeed, low-energy QCD is reduced to a Yukawa model, reducible yet to a Nambu-Jona-Lasinio model with all parameters properly fixed by QCD (see arxiv for this). But this is another story.

    About the low fuss that my work produced I do not know. But, since now, it was a great privilege to work these problems out, getting the results published on such important journals and rising the interest of a great mathematician like Terry is.
     
    Last edited by a moderator: May 4, 2017
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