Restoring the gauge invariance in non-Abelian second-class theories

TL;DR

This paper introduces a generalized gauge unfixing method to restore gauge invariance in non-Abelian second-class systems, enabling the reformulation of models like massive Yang-Mills and Skyrme models within a gauge-invariant framework.

Contribution

It presents a novel formalism that reformulates non-Abelian second-class systems directly in phase space, restoring gauge invariance in models such as SU(N) Yang-Mills and Skyrme.

Findings

Derived gauge invariant variables for non-Abelian models

Achieved gauge invariant Hamiltonians and first-class Lagrangians

Provided a formalism applicable to SU(N) and SU(2) models

Abstract

In this paper, we propose a generalization of an improved gauge unfixing formalism in order to generate gauge symmetries in the non-Abelian valued systems. This generalization displays a proper and formal reformulation of second-class systems within the phase space itself. We then present our formalism in a manifestly gauge invariant resolution of the $SU(N)$ massive Yang-Mills and $SU(2)$ Skyrme models where gauge invariant variables are derived allowing then the achievement of Dirac brackets, gauge invariant Hamiltonians and first-class Lagrangians.