Talk:Yang–Mills existence and mass gap

Suggest merge

I suggest Mass gap and Yang–Mills existence and mass gap should be merged together. Reason: both articles are quite short, but Yang–Mills existence and mass gap actually contains more background information. Merging them together should be perfectly possible. 131.111.8.96 01:34, 1 April 2007 (UTC)

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)

Proof by Dynin?

On May 30, User:Aldynin added this:

Alexander Dynin, "Energy-mass spectrum of Yang-Mills bosons is infinite and discrete", arXiv:0903.4727 [math-ph]. Contains a solution of the problem.

Could somebody please check this? --bender235 (talk) 11:44, 3 June 2010 (UTC)

Some remarks:

1. User:Aldynin probably has a WP:COI.
2. Primary source is not reliable for such a claim. Need reliable secondary of tertiary source to verify the claim being made.
3. 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)

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)

According to arXiv:1005.3779 Dynin's paper was "submitted to Journal of Mathematical Physics", by the way. --bender235 (talk) 12:34, 7 June 2010 (UTC)

I see no such mentions of submission, and this isn't the paper we are talking about. Also, submitted papers can be, and often are, rejected. So this preprint is pretty far from being considered a reliable source. Headbomb {talk / contribs / physics / books} 18:14, 16 June 2010 (UTC)

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)

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."?  --Lambiam 21:35, 6 June 2010 (UTC)

I think that would be a good idea. --bender235 (talk) 11:10, 7 June 2010 (UTC)

The preprint shouldn't be mentioned. That would give undue weight to Dynin's work. Headbomb {talk / contribs / physics / books} 11:30, 7 June 2010 (UTC)

But there isn't any other source, is it? --bender235 (talk) 12:15, 7 June 2010 (UTC)

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 (Александр С. Дынин) known from the Agranovich–Dynin theorem (see e.g. here), but I could be mistaken.  --Lambiam 17:28, 8 June 2010 (UTC)

SELF-INTRODUCTION OF A. DYNIN

Dear Lambiam,

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] —Preceding unsigned comment added by 69.212.82.176 (talk) 19:07, 21 November 2010 (UTC)

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)

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)

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., “Energy-mass spectrum of Yang-Mills bosons is infinite and discrete”, 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] —Preceding unsigned comment added by 68.250.186.163 (talk) 03:30, 21 November 2010 (UTC)

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 “Quantum Yang-Mills theory” 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)

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 “Quantum Yang-Mills theory” 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)

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. Prástaro, 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. Prástaro, 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.

[3] A. Prástaro, Quantum extended crystal PDE's. Nonlinear Studies 18(3)(2011), 447-485. arXiv: 1105.0166[math.AT]. MR2816182(2012k:57043); Zbl 1253.35135.

[4] A. Prástaro, 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. Prástaro, 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. Prástaro, 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. Prástaro. In fact they talk about a quantum Yang-Mills equation on an affine space-time. With this respect, the Prástaro'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. Prástaro. 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 !

(Agostino.prastaro (talk) 11:47, 5 July 2013 (UTC))

While your effort should be appreciated, the claim must be supported by the scientific community. In order to get an idea about the way things work you should look at the history of Grigori Perelman and the Poincaré conjecture. If all the community will agree that you have found a proof you are done and the way to glory is open. Otherwise you should act like any other colleague with a similar claim trying to publicize your work with conferences and further publications to elucidate better the content of your work.--Pra1998 (talk) 16:32, 5 July 2013 (UTC)

Yet another claim

http://www.youtube.com/watch?v=3zdqSg0ZxDs — Preceding unsigned comment added by 84.158.152.168 (talk) 10:48, 12 October 2013 (UTC)

Check this to see how to understand this claim.--Pra1998 (talk) 17:22, 13 October 2013 (UTC)

added material on Dynin's paper

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)

Unfortunately, even modified Wightman axioms (see, e.g., Bogoliubov (1990), 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), Chapter 6 and Appendix A.2].

However, Alexander Dynin Dynin (2014) 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 Lite Wilczek (2004), pp. 79–98.

This paper is currently under discussion at Physics Overflow.--Pra1998 (talk) 12:26, 9 August 2014 (UTC)

Dealing with WP:OR and WP:PROMO

Do note that WP:TPO permits/encourages the deletion of promotional material on Talk pages. Choor monster (talk) 11:29, 7 June 2015 (UTC)

A place in the section "Wightman axioms" not clear

I don't understand what is meant here:

The Wightman axioms require that the Poincaré group acts unitarily on the Hilbert space. In other words, they have position dependent operators called quantum fields which form covariant representations of the Poincaré group.

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?

Mamuka Jibladze (talk) 13:25, 14 April 2016 (UTC)

adding meaning of \langle f(x) g(z) \rangle

The body currently contains the notation

$\langle \phi (0,t)\phi (0,0)\rangle$

Can the page link to or define this? If there were a comma between \phi(0,t)and \phi(0,0) it would look like an inner product to me. But there isn't in several locations this equation is included. 0¹⁸ (talk) 04:49, 10 August 2024 (UTC)