Gauge invariance and dual equivalence of Abelian and non-Abelian actions via dual embedding formalism

TL;DR

This paper explores a dual embedding formalism to establish gauge invariance in Abelian and non-Abelian theories, providing a systematic method that avoids ambiguity and extends previous approaches, with many novel results presented.

Contribution

It introduces a dual embedding formalism that effectively converts noninvariant theories into gauge invariant ones for both Abelian and non-Abelian systems, avoiding ambiguity issues of prior methods.

Findings

Successfully applied to Abelian theories

Extended to non-Abelian theories without modifications

Most results are novel or presented from a new perspective

Abstract

The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is always desirable to have a bridge between gauge invariant and noninvariant theories. Once established, this kind of mapping between first-class (gauge invariant) and second-class systems, in Dirac's formalism can be considered as a sort of duality. In this paper we investigate this "duality" obtaining a gauge invariant theory starting with a noninvariant one. We analyzed both Abelian and non-Abelian theories and the procedure used is the recent dual (also called symplectic) embedding formalism. We believe that this method is the most convenient one since it is not plagued by the ambiguity problems that torments BFFT and other iterative methods. We demonstrated exactly that this "dualization" method used here does not require any special modification to handle with non-Abelian systems, which is also a new result described in this paper. To prove the gauge invariance we used just the Dirac constraint technique. It is relevant to say here that, although this work is lengthy, the majority of the results presented here are new in the literature. The results that are not new were reproduced within a new perspective.