Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories

TL;DR

This paper presents an algebraic method based on the action principle to derive gauge transformations in gauge theories, avoiding path integrals and delta functionals, with potential applications to non-abelian and supersymmetric theories.

Contribution

It introduces a novel algebraic approach to gauge transformations that bypasses traditional path integral techniques, applicable to both abelian and non-abelian gauge theories.

Findings

Derived gauge transformations algebraically from the action principle.

Established a method to connect Coulomb and covariant gauges without path integrals.

Potential applicability to supersymmetric and non-abelian gauge theories.

Abstract

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to the celebrated Fock-Schwinger (FS) gauge for the abelian (QED) gauge theory without recourse to path integrals or to commutation rules and without making use of delta functionals. The interest in the FS gauge, in particular, is that it leads to Faddeev-Popov ghosts-free non-abelian gauge theories. This method is expected to be applicable to non-abelian gauge theories including supersymmetric ones.