Gauge Freedom in Path Integrals in Abelian Gauge Theory

TL;DR

This paper explores the extension of gauge symmetry in Abelian gauge theories through a two-step gauge recovery process, leading to a novel gaugeon formalism that incorporates quantum gauge degrees of freedom.

Contribution

It introduces a method to extend gauge symmetry in Abelian theories using the Harada--Tsutsui procedure, resulting in a new gaugeon formalism with quantum gauge degrees of freedom.

Findings

Recovered gauge symmetry by introducing an additional field.

Derived a theory equivalent to the extended Type I gaugeon formalism.

Demonstrated the applicability of the two-step gauge recovery process.

Abstract

We extend gauge symmetry of Abelian gauge field to incorporate quantum gauge degrees of freedom. We twice apply the Harada--Tsutsui gauge recovery procedure to gauge-fixed theories. First, starting from the Faddeev--Popov path integral in the Landau gauge, we recover the gauge symmetry by introducing an additional field as an extended gauge degree of freedom. Fixing the extended gauge symmetry by the usual Faddeev--Popov procedure, we obtain the theory of Type I gaugeon formalism. Next, applying the same procedure to the resulting gauge-fixed theory, we obtain a theory equivalent to the extended Type I gaugeon formalism.