Whether the vacuum manifold in the Minkowskian non-Abelian model quantized by Dirac can be described with the aid of the superselection rules?

Abstract

We intend to show that the vacuum manifold inherent in the Minkowskian non-Abelian model involving Higgs and Yang-Mills BPS vacuum modes and herewith quantized by Dirac can be described with the help of the superselection rules if and only if the "discrete" geometry for this vacuum manifold is assumed (it is just a necessary thing in order justify the Dirac fundamental quantization scheme applied to the mentioned model) and only in the infinitely narrow spatial region of the cylindrical shape where topologically nontrivial vortices are located inside this discrete vacuum manifold.