in an old paper, Boris P. Kosyakov discusses exact solution of Yang-Mills-Wong Theory, and his paper seems to indicate that it is possible to study quark confinement from exact solution of Yang-Mills-Wong theory. What do you think?
http://arxiv.org/pdf/hep-th/9902039.pdf
I don't know exactly what the Wong part consists of, but it seems to be the addition of a finite number of scalar (color-)charged particles. In that case I think it is absolutely impossible to find any trace of confinement in the classical theory (CCD). My reason for that is the scale invariant property of a pure Yang-Mills theory. Confinement will necessarily involve a length scale. Thus, one of the first things to search for is the source of a confinement scale; how can you find such a source in a purely classical theory (at zero temperature)?
Historically, there have been many attempts to describe the QCD vacuum by quasi-classical methods. I remember it was a rather big industry in the early 1980's, connected with names like the Saviddy vacuum, the Copenhagen vacuum, etc. Before that, use of exact (or almost-exact) solutions of the imaginary time Yang-Mills equations (instantons, merons) were also attempted. But never in a purely classical context, only as some hypothetically important contributions to the QCD functional integral.
I think it is fair to say that none of these attempts lead to a successful description of QCD (in four space-time dimensions). It is not very likely that more attempts in exactly the same direction will succeed either.
I don't know exactly what the Wong part consists of, but it seems to be the addition of a finite number of scalar (color-)charged particles. In that case I think it is absolutely impossible to find any trace of confinement in the classical theory (CCD). My reason for that is the scale invariant property of a pure Yang-Mills theory. Confinement will necessarily involve a length scale. Thus, one of the first things to search for is the source of a confinement scale; how can you find such a source in a purely classical theory (at zero temperature)?
Historically, there have been many attempts to describe the QCD vacuum by quasi-classical methods. I remember it was a rather big industry in the early 1980's, connected with names like the Saviddy vacuum, the Copenhagen vacuum, etc. Before that, use of exact (or almost-exact) solutions of the imaginary time Yang-Mills equations (instantons, merons) were also attempted. But never in a purely classical context, only as some hypothetically important contributions to the QCD functional integral.
I think it is fair to say that none of these attempts lead to a successful description of QCD (in four space-time dimensions). It is not very likely that more attempts in exactly the same direction will succeed either.
@Kare: Thank you for your comments.
@Mohamed: Thank you, I will read your paper: A new look at quarks confinement
It's useful to actually read Kosyakov's paper. It studies the properties of a finite number of spinless particles, interacting with a non-abelian gauge field. This doesn't have anything to do with quarks-since the particles in question don't carry spin-and it doesn't have anything to do confinement, since the bound states, the clusters constructed, aren't singlets of the gauge group-thye're charged. And it doesn't describe a field theory of matter, since the number of particles is fixed-which leads to other problems, too, from the ``no interaction theorem''. So it isn't useful in understanding quark confinement, which is the fact that the color singlet states of a field theory are favored.
Dear Victor,
in my opinion the confinement problem of quarks is strictly related to the quantum character of these particles. In http://arxiv.org/abs/1205.2894 (part II) I have given a general method to test whether a solution of quantum super Yang-Mill PDEs encodes confined quantum particles. In my theory quantum particles (quarks ...) are not point-like, therefore solutions are interpreted as nonlinear quantum propagators.
Instead you refer to a complete classic formulation, and your quarks are point-like there. Of course you can also study the confinement problem in such a called YMW-framework (I looked to the paper...), but the conclusions cannot pretend to be realistic ... it is a simple amusing toy.
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