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No because Mass gap also has uses in condensed matter physics.
TriTertButoxy (
talk) 17:09, 6
March 2012 (UTC)
NO!
DO NOT MERGE THEM TOGETHER. IT IS A MILLENIUM PROBLEM AND THEY SHOULD BE ON THEIR OWN PAGES.
Agree. Do not merge.
By the way, from this article one can well estimate the difference in mathematical rigor involved, and also the positive, and partially negative consequences: negative, because mathematicians are naturally always behind, which is one side of the coin. - With regards,
132.199.101.108 (
talk)
12:49, 14 April 2009 (UTC)reply
Primary source is not reliable for such a claim. Need reliable secondary of tertiary source to verify the claim being made.
The fact that such a landmark claim has not yet been published in a peer-reviewed journal, is indicative that the article has been found flawed and has been rejected at peer-review.
TimothyRias (
talk)
12:57, 3 June 2010 (UTC)reply
I agree with TimRias here. Although on #3, it could also be indicative that the author hasn't yet submitted the paper, or that the arxiv hasn't yet updated this entry with the published paper (upon checking, this only exists in an unreviewed preprint form). Either way, for a claim as big as that one, we'd at the very least need a review from one of the top-level publications such as Journal of Physics or Physical Review or something equivalent. Headbomb {
talk /
contribs /
physics /
books}17:52, 3 June 2010 (UTC)reply
arXiv:
1005.3779 says "Dynin, A., Energy-mass spectrum of Yang-Mills bosons is infinite and discrete, arXiv:math-ph/09034727 (submitted to Journal of Mathematical Physics)." And no, I did not intend to say that this means Dynin's proof is rock-solid. I just wanted to mention that the paper is submitted and could appear in a peer-reviewed journal soon. And yes, I do know that papers occasionally get rejected. --
bender235 (
talk)
12:25, 17 June 2010 (UTC)reply
Rather than adding this "point blank" as a reference, could it be a reference in a section with a title such as "Claimed proof", and a text such as "In May 2009, Alexander Dynin, professor at the Department of Mathematics of
Ohio State University, claimed to have given a rigorous proof that the energy-mass spectrum of Yang-Mills bosons is infinite and discrete.[ref here] If strenuous verification of the purported proof does not turn up any serious flaw or gap, this then solves the Millenium Prize Problem of the Clay Mathematics Institute. To be accepted as such under the rules for the Millennium Prizes, not only must a paper presenting a proposed solution be accepted for publication in a refereed mathematics journal of world-wide repute, but the solution must also still enjoy general acceptance in the mathematics community two years after publication."? Â --
Lambiam21:35, 6 June 2010 (UTC)reply
I'm not sure how
WP:UNDUE applies to this case. The policy is about giving undue weight to one point of view among several. What are the other points of view? Does anyone else claim to have a solution, or do you know of someone challenging Dynin's claim? I suspect the author is the same Dynin as the former Soviet mathematician
Alexander S. Dynin (ĐлДĐșŃĐ°ĐœĐŽŃ Х. ĐŃĐœĐžĐœ) known from the AgranovichâDynin theorem (see e.g.
here), but I could be mistaken. Â --
Lambiam17:28, 8 June 2010 (UTC)reply
I was a student of great I. Gelfand, who, universal as he was, had a special
predilection for mathematical physics, an important subject at his
celebrated mathematical seminar in Moscow. In particular, he invented path integral
independently of Feynman but, unfortunately rejected by caustic L. Landau and his cohort of physicists.
50 years ago in my PH. D. dissertation I made important inroads to a
solution of Gelfand Index Problem. The work got the prize of Moscow
Mathematical Society and, more importantly, used by Atiyah and Singer in
their first solution of the Gelfand problem. Certainly, an immature student
had no chance in competition with the grandmasters,
but afterwards my younger friend S. Novikov (the great
topologist and mathematical physicist) regretted that he did not pay more
attention to my questions during our
graduate school time. Otherwise the famous Atiyah-Singer index theorem
might have different names.
Gelfand influence is apparent in my YM paper. Actually the paper applies
a rather non-conventional
but rigorous mathematical QFT based on Gelfand triples from 55 years ago
as well as on Hida white noise calculus. Most of my difficulties with
(math) physicists are due to the conflict with their paradigms. Just as in the
Gelfand-Landau case! --[User:Aldynin] âPreceding
unsigned comment added by
69.212.82.176 (
talk)
19:07, 21 November 2010 (UTC)reply
So far, this is all unpublished work. When it gets published in a reputable journal, (J Math Phys would certainly qualify as that, if it ends up there), Dynin's work can be mentioned, but not before. Headbomb {
talk /
contribs /
physics /
books}18:14, 16 June 2010 (UTC)reply
Dear
Lambiam, I am sorry to inform you that
Marco Frasca has a proof published in two reputable journals :
Physics Letters B and
Modern Physics Letters A. The latter publication, was prompted after a criticism by
Terence Tao, and has been agreed with Terry as being correct for the criticized part regarding a theorem mapping a
scalar field theory and
Yang-Mills theory (see
here). I have avoided to put these papers here because, until someone in the community will accept the claim as correct, and it is, I will not do that. Frasca get the exact spectrum being the one of a
quantum harmonic oscillator well verified in
lattice computations and the corresponding
propagator in the proper low-energy limit also in agreement with lattice computations. As a Wiki's editor I will avoid to insert these papers until some relevant support will come out.--
Pra1998 (
talk)
19:34, 16 June 2010 (UTC)reply
ON THE M. FRASCA PAPER
Surprise: It has been an experts opinion that the YM mass gap problem is beyond perturbation theory.
Interestingly, the leading term of M. Frasca asymptotics of quantum YM energy spectrum is a harmonic oscillator spectrum. This echoes the spectrum estimate from below given in Dynin, A.,
âEnergy-mass spectrum of Yang-Mills bosons is infinite and discreteâ, arXiv:math- ph/09034727. That paper was submitted to Journal of Mathematical Physics in May 2009 but withdrawn after 18 months of their indecision. Currently a purified version is in preparation for an appropriate mathematical journal.--[User:Aldynin] âPreceding
unsigned comment added by
68.250.186.163 (
talk)
03:30, 21 November 2010 (UTC)reply
References 43 and 45 unspecified.
I found ref 43 link
[1] on adsabs but there is no free to read article. Also found ref 45 on Google books
[2]. The Jaffe and Witten âQuantum Yang-Mills theoryâ reference contains these references with the numbered citations. Adding them with cite journal and cite book would improve the article a little, but only if someone also can read and check the relevance of the references.
Puzl bustr (
talk)
16:04, 11 May 2012 (UTC)reply
References 43 and 45 unspecified.
I found ref 43 link
[3] on adsabs but there is no free to read article. Also found ref 45 on Google books
[4]. The Jaffe and Witten âQuantum Yang-Mills theoryâ reference contains these references with the numbered citations. Adding them with cite journal and cite book would improve the article a little, but only if someone also can read and check the relevance of the references.
Puzl bustr (
talk)
16:04, 11 May 2012 (UTC)reply
Yang-Mills Existence and Mass-Gap Problem: A solution in Quantum Super PDEs Algebraic Topology
The Yang-Mills existence and mass gap problem, has been completely solved in the paper [1]. (These results were also partially announced in some already published works by the same author.)
[1] A. PrĂĄstaro, Quantum extended crystal super PDE's. Nonlinear Analysis. Real World Appl. 13(6)(2012), 2491-2529.
See also the complementary papers [2-6] and related works quoted therein.
[2] A. PrĂĄstaro, Quantum exotic PDE's. Nonlinear Analysis. Real World Appl. 14(2)(2013), 893-928. DOI: 10.1016/j.nonrwa.2012.04.001. arXiv: 1106.0862[math.AT]. MR2991123.
[4] A. PrĂĄstaro, Strong reactions in quantum super PDE's. I: Quantum hypercomplex exotic super PDE's. arXiv: 1205.2894[math.AT]. (Part I and Part II are unified in arXiv.)
[5] A. PrĂĄstaro, Strong reactions in quantum super PDE's. II: Nonlinear quantum propagators. arXiv: 1205.2894[math.AT]. (Part I and Part II are unified in arXiv.)
[6] A. PrĂĄstaro, Strong reactions in quantum super PDE's. III: Exotic quantum supergravity. arXiv: 1206.4856[math.AT].
It is important to emphasize that the YM-problem introduced by A. Jaffe and E. Witten concerns a particular aspect of the general theory formulated in the previous works by A. PrĂĄstaro. In fact they talk about a quantum Yang-Mills equation on an affine space-time. With this respect, the PrĂĄstaro's algebraic topologic method to classify global solutions of quantum super PDEs, explicitly applied to the quantum super Yang-Mills PDEs, allows to solve the quoted problem as introduced by A. Jaffe and E. Witten.
In particular look to Theorem 3.14 and Theorem 3.28 in [1].
Warn ! Even if the considered problem concerns in a sense Classical Mathematical Physics, in order to be solved it necessitates a new algebraic topologic theory of quantum super PDEs, as already formulated by A. Pråstaro. In fact, the great difficulty of the problem is just in the impossibility to solve it remaining in the old usual framework of the quantum field theory !
The following text was on the page, as an edited form of comments on Dynin's paper. Before it goes back on the page, it presumably should be discussed.
Charles Matthews (
talk)
09:56, 14 July 2014 (UTC)reply
Unfortunately, even modified Wightman axioms (see, e.g.,
Bogoliubov (1990) harvtxt error: no target: CITEREFBogoliubov1990 (
help), Chapter 10, conflict with the simplest cases of Gupta-Bleuler theory of quantum electromagnetic fields, as well as with common local renormalizable gauges (see, e.g.
Strocchi (1964) harvtxt error: no target: CITEREFStrocchi1964 (
help), Chapter 6 and Appendix A.2].
However, Alexander Dynin
Dynin (2014) harvtxt error: no target: CITEREFDynin2014 (
help) presents a rigorous relativistic quantum Yang-Mills theory in his framework of pseudodifferential operators with functional derivatives. It is shown that the spectra of quantum Yang-Mills energy-mass operators with spacial cutoffs are sequences of their eigenvalues converging to plus infinity. In particular, the cutoff operators have positive spectral mass gaps, in agreement with Yukawa principle that a confinement implies a positive mass. The spectra are self-similar in the inverse proportion to the running coupling constant. More generally, these spectral properties hold for quantum interactions of Yang-Mills bosons with chiral 1/2 spin fermions (
QCD LiteWilczek (2004) harvtxt error: no target: CITEREFWilczek2004 (
help), pp. 79â98.
Specifically, I don't understand what the word "they" refers to. Unfortunately I am not a specialist, I rather came to this page to learn something, so I cannot edit this place myself. However I am sure something's wrong with that place - simply grammatically it is inconsistent if I am not mistaken. Could somebody please elucidate this, and/or edit the text accordingly?
...After a while I realized that there is in fact a grammatically correct interpretation of the text. Namely, "they" might mean "the axioms" here. However I believe then the contents is unclear. "The axioms have operators" - what does this actually mean?