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What's the current state of Yang–Mills mass gap question, is there any place that does this problem? Especially I want to know if there is any progress (out of that mentioned in the introduction article by Witten and Jaffe). Is it too hard for a mathematician? Thanks!

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There's some guidelines about open problems in the FAQ that you might want to read, but there was a good article by Faddeev last November that you should know about:

Mass in Quantum Yang-Mills Theory, by Faddeev

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There is a rather strange situation here because a russian mathematician, Alexander Dynin, is claiming to have solved it. Please, refer to this question of mine or this paper published in a reputable journal. Till now I have not seen any reaction from the community but I think that an analysis of the work of this author is overdue. Indeed, he has worked on this since 2009 as I can see from arxiv.

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For the 3D version of the proble, see

[1] Dimitra Karabali and V. P. Nair, Int. J. Mod. Phys. A 12, 1161 (1997) http://arxiv.org/abs/hep-th/9610002

See eqn (20), (21) and the following paragraph.

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    $\begingroup$ While it provides some explanations, the problem treated there is in 3 dimensions only, while the Clay Millennium problem asks for a solution in 4 dimensions, where extra difficulties show up. $\endgroup$ Apr 4, 2015 at 16:24
  • $\begingroup$ I forgot to mention 3D. Thanks for the correction. $\endgroup$ May 29, 2015 at 21:55

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