The claim in the paper is wrong, unfortunately, and the paper is fundamentally ill-concieved. This, even though it comes from a justly respected author with a prior history of valuable contributions.
There is no formalism for constructing quantum Yang-Mills theory starting from any sort of global classical solution, and there simply cannot be (it might be possible locally, at short distances, but then all the issues are in pasting together the quantum theory from the local near-classical descriptions).
Quantum Yang Mills is a well-defined computational thing, the Euclidean version can be computed on a Lattice. The continuum action is $1/g^2 \mathrm{tr} F^2$, the lattice action replaces $F^2$ by the holonomy of the link variables over each plaquette. The coupling plays the role of $\hbar$, and the $\hbar\rightarrow 0$ limit is exactly the weak coupling limit, or zero coupling limit, where the gauge group turns into a bunch of noninteracting vector bosons. It is also the small-lattice limit, because of asymptotic freedom. The continuum classical equations locally (meaning at scales which are exponentially teeny tiny) are solutions of zero coupling Yang-Mills theory. They have no relation to the behavior at longer distances, where the coupling runs stronger.
So any procedure which starts with the classical solutions and tries to do some formal jiggling to produce "solutions" to quantum Yang Mills by formally defining operators is always infinitely far away from the quantum vacuum of Yang-Mills. It is solving equations which have a fixed coupling independent of scale to describe a system which does not have a fixed coupling independent of scale. So it can never work.
But Dynin claims it does work! Why? It's because he is doing something completely different, something which has no relation to what is normally called Euclidean Yang-Mills theory, and misinterpreting this alternate construction as a quantization of Yang-Mills theory.
What he is doing is using a well-known stochastic formalism which is a known mathematician-obfuscated version of the physicist's Euclidean creation and annihilation operators, and applying it to configurations of initial data, which he identifies as classical solutions of Yang-Mills theory. The result of this is associating a creation and annihilation operator to each classical solution, producing a tower of free bosons sitting on top of each initial data. These quanta have no relation to any excitations in actual quantum Yang-Mills, they are simply a mathematical artifact of this construction. These quanta are indexed by classical solutions, not by fluctuations of the true Euclidean vacuum.
He then defines a nonsensical energy for his model, which preserves the N=0 state free-vacuum as the interacting vacuum (I made a false claim here initially). I speculate that this mistake is due to the fact that mathematicians don't have experience with simulations of Lattice Yang-Mills theory. Such simulations produce a valuable picture, first developed by Kenneth Wilson, and without it, one is lost, and can easily go down a path very distant from any correct one.
The vacuum of quantum Yang-Mills is calculated on the Lattice and it is described accurately by small perturbations to Wilson's strong coupling fixed point. The strong coupling limit is $g\rightarrow\infty$, or $\hbar\rightarrow\infty$, where the lattice action is zero. Zero action means that every link matrix is equally likely and completely independent. This is the description of Yang-Mills at long distances, as known for sure from even the very first lattice studies by Wilson. If you perturb this by introducing perturbations, slight correlations between neighboring link-matrices, these die off exponentially, and the leading approximation to a long Wilson-loop action is by the minimal surface spanning the loop. This behavior, discovered by Kenneth Wilson, is what led confinement to become universally accepted in physics.
This behavior is quite simple to understand, and the basic problem of Yang-Mills mass-gap is simply to prove rigorously that the Yang-MIlls lattice field randomizes in this way, even when at short distances, the path integral is dominated by configurations which are close to classical solutions. The problem of existence is simply to show that the limit of small lattice spacings can be taken, using a coupling which vanishes as the perturbative running of the coupling at small distances, the statistical fluctuations at long-distances converge.
This paper simply cannot do this, because the method is starting from classical solutions to classical Yang-Mills. There is no useful relation between global solutions of Yang-Mills and quantum Yang-Mills, because the classical global solutions are globally correlated--- the classical data on an initial slice uniquely determines the solution at all future times--- while the quantum system has all the correlations dying off exponentially at a distance scale of $1/\Lambda$. So the initial approximation has a structure which is infinitely far from the correct totally random structure at long distances, and the approach is fundamentally misunderstanding the classical correspondence in the confining infinitely strong interaction limit of long distances, I am sorry to say.
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