"Discrete" vacuum geometry as a tool for Dirac fundamental quantization of Minkowskian Higgs model

Abstract

We demonstrate that assuming the "discrete" vacuum geometry in the Minkowskian Higgs model with vacuum BPS monopole solutions can justify the Dirac fundamental quantization of that model. The important constituent of this quantization is getting various rotary effects, including collective solid rotations inside the physical BPS monopole vacuum, and just assuming the "discrete" vacuum geometry seems to be that thing able to justify these rotary effects. More precisely, assuming the "discrete" geometry for the appropriate vacuum manifold implies the presence of thread topological defects (side by side with point hedgehog topological defects and walls between different topological domains) inside this manifold in the shape of specific (rectilinear) threads: gauge and Higgs fields located in the spatial region intimately near the axis $z$ of the chosen (rest) reference frame. This serves as the source of collective solid rotations proceeding inside the BPS monopole vacuum suffered the Dirac fundamental quantization. It will be argued that indeed the first-order phase transition occurs in the Minkowskian Higgs model with vacuum BPS monopoles quantized by Dirac. This comes to the coexistence of two thermodynamic phases inside the appropriate BPS monopole vacuum. There are the thermodynamic phases of collective solid rotations and superfluid potential motions.