Gauge Freedom in the Path Integral Formalism

TL;DR

This paper explores gauge freedom in the path integral formalism, extending gauge symmetry to interpret 't Hooft's gauge parameter change and connecting it with gaugeon formalisms for covariant non-abelian gauge theories.

Contribution

It introduces an extended gauge symmetry framework that unifies 't Hooft averaging with gaugeon formalism, providing a new gauge covariant formulation of non-abelian gauge theories.

Findings

Extended gauge symmetry formulation of 't Hooft averaging.

Connection between 't Hooft average and gaugeon formalism.

Gauge covariant non-abelian gauge theory formulation.

Abstract

We investigate 't Hooft's technique of changing the gauge parameter of the linear covariant gauge from the point of view of the path integral with respect to the gauge freedom. Extension of the degrees of freedom allows us to formulate a system with extended gauge symmetry. The gauge fixing for this extended symmetry yields the 't Hooft averaging as a path integral over the additional degrees of freedom. Another gauge fixing is found as a non-abelian analogue of the type II gaugeon formalism of Yokoyama and Kubo. In this connection, the 't Hooft average can be viewed as the analogue of the type I gaugeon formalism. As a result, we obtain gauge covariant formulations of non-abelian gauge theories, which allow us to understand 't Hoot's technique also from the canonical fromalism.