Practical scheme of reduction to gauge invariant variables

TL;DR

This paper presents a practical reduction scheme to gauge invariant variables for systems with first class constraints, applying it to electrodynamics, Yang-Mills theory, and an $SU(2)$ model to explore confinement mechanisms.

Contribution

It introduces a new reduction scheme based on restricted 1-forms, applicable to gauge theories, and demonstrates its use in models including confinement analysis.

Findings

Reduction scheme effectively isolates gauge invariant variables.

Application to electrodynamics and Yang-Mills models shows practical utility.

Finite $SU(2)$ model suggests possible confinement mechanisms.

Abstract

For systems with first class constraints the reduction scheme to the gauge invariant variables is considered. The method is based on the analysis of restricted 1-forms in gauge invariant variables. This scheme is applied to the models of electrodynamics and Yang-Mills theory. For the finite dimensional model with $SU(2)$ gauge group of symmetry the possible mechanism of confinement is obtained.