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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)
March 2012 (UTC)
DO NOT MERGE THEM TOGETHER. IT IS A MILLENIUM PROBLEM AND THEY SHOULD BE ON THEIR OWN PAGES.
Agree. Do not merge.
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)
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)
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)
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)
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)
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.)
( Agostino.prastaro ( talk) 11:47, 5 July 2013 (UTC))
http://www.youtube.com/watch?v=3zdqSg0ZxDs — Preceding unsigned comment added by 84.158.152.168 ( talk) 10:48, 12 October 2013 (UTC)
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)
Do note that WP:TPO permits/encourages the deletion of promotional material on Talk pages. Choor monster ( talk) 11:29, 7 June 2015 (UTC)
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)
This
level-5 vital article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||
|
Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
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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)
March 2012 (UTC)
DO NOT MERGE THEM TOGETHER. IT IS A MILLENIUM PROBLEM AND THEY SHOULD BE ON THEIR OWN PAGES.
Agree. Do not merge.
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)
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)
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)
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)
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)
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.)
( Agostino.prastaro ( talk) 11:47, 5 July 2013 (UTC))
http://www.youtube.com/watch?v=3zdqSg0ZxDs — Preceding unsigned comment added by 84.158.152.168 ( talk) 10:48, 12 October 2013 (UTC)
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)
Do note that WP:TPO permits/encourages the deletion of promotional material on Talk pages. Choor monster ( talk) 11:29, 7 June 2015 (UTC)
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)