Path Integrals, BRST Identities and Regularization Schemes in Nonstandard Gauges

TL;DR

This paper investigates path integrals in Coulomb-like gauges, reproduces Christ-Lee operator ordering terms, discovers new fermionic operator terms, and proposes a regularization scheme preserving BRST symmetry and avoiding energy divergences.

Contribution

It introduces a regularization scheme that maintains BRST invariance and addresses operator ordering issues in nonstandard gauges within path integral formalism.

Findings

Reproduction of Christ-Lee terms within path integrals.

Discovery of new fermionic operator terms.

Proposal of a BRST-preserving regularization scheme.

Abstract

The path integral of a gauge theory is studied in Coulomb-like gauges. The Christ-Lee terms of operator ordering are reproduced {\it{within}} the path integration framework. In the presence of fermions, a new operator term, in addition to that of Christ-Lee, is discovered. Such kind of terms is found to be instrumental in restoring the invariance of the effective Lagrangian under a field dependent gauge transformation, which underlies the BRST symmetry. A unitary regularization scheme which maintains manifest BRST symmetry and is free from energy divergences is proposed for a nonabelian gauge field.