Interpreting Dirac variables in terms of the Hilbert space of gauge-invariant and Poincare-covariant states

TL;DR

This paper explores the representation of Dirac variables within gauge-invariant, Poincare-covariant states in Abelian and non-Abelian models, and conjectures about symmetry breaking and charge preservation in specific gauge theories.

Contribution

It provides a Hilbert space framework for Dirac variables in gauge theories and introduces a conjecture on symmetry breaking and charge conservation in Abelian models.

Findings

Hilbert space description of Dirac variables in gauge models

Conjecture on U(1) symmetry breaking to Z and charge preservation

Framework applicable to both Abelian and non-Abelian gauge theories

Abstract

The goal of this note is to give a description of Dirac variables in Abelian as well as non-Abelian gauge models in terms of gauge-invariant and Poincare-covariant states sweeping a Hilbert space ${\cal H}_{\rm vac}$. The next our conjecture concerns the spontaneous breakdown of the Abelian U(1) symmetry in the 'discrete' $U(1)\to {\bf Z}$ wise. We suppose that gauge charges are preserved in this case.