Some explanation about Dynin's formalism I have seen this claim on the Wikipedia page for the Yang-Mills Millenium problem by Alexander Dynin. He is a mathematician working at the Department of Mathematics of Ohio State University and so, I think his should represent respectable work. The question is that I am a physicist and I have not the right knowledge to approach Dynin's work. Please, could you give me some hints and references about so I can make an idea by myself of these techniques? My aim is to get a comparison with the work currently pursued in the area of theoretical physics about this same problem.
Thanks a lot beforehand.
 A: The paper is currently (and will be at least for a few days) under discussion at
http://www.physicsoverflow.org/21786/energy-mass-spectrum-yang-mills-bosons-infinite-and-discrete
A: I reviewed at 
http://www.physicsoverflow.org/21786/energy-mass-spectrum-yang-mills-bosons-infinite-and-discrete?show=21846#a21846
four nearly identical unpublished papers by Dynin on the Clay millennium problem. The most recent paper claims at  the beginning of Section 1:
``A mathematically rigorous solution is given for both parts of the
7th Millennium problem of Clay Mathematics Institute''
As I discuss in my review, his claim is wrong. Neither are the explicit requirements of the problem definition satisfied (no discussion of Poincare invariance and causality), nor is the paper mathematically rigorous in a crucial part of the construction (it is not proved that there is an operator with the anti-normal symbol specified in the construction). 
The main criticism also applies to the published paper 
Alexander Dynin,
Quantum Yang-Mills-Weyl Dynamics in Schroedinger paradigm,
Russian Journal of Mathematical Physics 21 (2014),No.2,169-188.
http://arxiv.org/abs/1005.3779
which wrongly claims to give a construction of massless QED.
Note that there are other attempts in the literature to settle this millennium problem or variants of it.
Simone Farinelli, Four Dimensional Quantum Yang-Mills Theory and Mass Gap I: Quantization of the Solution of the Classical Equation, claimed to prove a mass gap given existence of a quantum Yang-Mills theory. This claim was reviewed at http://www.physicsoverflow.org/21788 and also found wanting.
Agostino Prastaro, Quantum Extended Crystal Super Pde's, claimed to have quantized a super-Yang-Mills theory with mass gap; see Theorem 3.28. An invitiation to review the claim is at http://www.physicsoverflow.org/21787 .
A: Here is the answer by Alexander Dynin to the preceding criticisms that I post on his behalf. I cannot post it as a comment being too long. A point of view from mathematicians would be helpful at this point.

The Schroedinger paradigm in QFT is a quantization of functionals on
  the initial data. Under certain conditions the latter parametrize the
  solutions of classical YM equations but not the latter are quantized.
  Functionals may be non-linear but the Shroedinger operator is linear
  of course. No disentanglement is required. 
Certainly, my procedure  is not relativistic but the energy-mass
  component of the classical relativistic  energy-momentum vector is not
  either. That is very important. In particular,  Poincare generators
  have no role here even when an  action functional is relativistic. The
  results are the same qualitatively in all  Lorentz coordinates. 
The energy-mass functional is a tame polynomial in infinite
  dimensions. As such it is a symbol of a tame operator in the 
  Gelfand-Kree triple and defines an unbounded self-adjoint operator in
  the corresponding Fock space. As such  the quantum Yang-Mills operator
  does exist.  My latest main theorem about the structure of its
  spectrum achieves  much more  than a solution of the YM mass gap
  problem.
Alexander

