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

TL;DR

This paper explores whether the vacuum manifold in a Minkowskian non-Abelian model quantized by Dirac can be characterized using superselection rules, contingent on a discrete geometric structure and specific spatial conditions.

Contribution

It demonstrates the conditions under which superselection rules can describe the vacuum manifold in a Dirac-quantized non-Abelian model, emphasizing the role of discrete geometry and vortex localization.

Findings

Superselection rules can describe the vacuum manifold under specific geometric assumptions.

Discrete geometry is necessary for Dirac quantization of the vacuum manifold.

Topologically nontrivial vortices are confined to a narrow cylindrical region.

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.