Superfluidity of Minkowskian Higgs vacuum with BPS monopoles quantized by Dirac may be described as Cauchy problem to Gribov ambiguity equation

TL;DR

This paper links superfluid properties of the Minkowskian Higgs vacuum with BPS monopoles to the Cauchy problem of the Gribov ambiguity equation, providing a gauge fixing perspective on topological monopole solutions.

Contribution

It demonstrates that the superfluid behavior can be described through the Cauchy problem for the Gribov ambiguity equation, connecting gauge fixing, topological monopoles, and vacuum structure.

Findings

Superfluid properties relate to solutions of the Gribov ambiguity equation.

The Cauchy problem fixes the covariant Coulomb gauge at initial time.

Vacuum BPS monopoles are solutions to the Gribov ambiguity equation.

Abstract

We show that manifest superfluid properties of the Minkowskian Higgs model with vacuum BPS monopoles quantized by Dirac may be described in the framework of the Cauchy problem to the Gribov ambiguity equation. The latter equation specifies the ambiguity in choosing the covariant Coulomb (transverse) gauge for Yang-Mills fields represented as topological Dirac variables, may be treated as solutions to the Gauss law constraint at the removal of temporal components of these fields. We demonstrate that the above Cauchy problem comes just to fixing the covariant Coulomb gauge for topological Dirac variables in the given initial time instant $t_0$ and finding the solutions to the Gribov ambiguity equation in the shape of vacuum BPS monopoles and excitations over the BPS monopole vacuum referring to the class of multipoles. The next goal of the present study will be specifying the look of Gribov topological multipliers entering Dirac variables in the Minkowskian Higgs model quantized by Dirac, especially at the spatial infinity, $| {\bf x} | \to \infty$ (that corresponds to the infrared region of the momentum space).