BRST Cohomology and Hilbert Spaces of Non-Abelian Models in the Decoupled Path Integral Formulation

TL;DR

This paper clarifies how to determine the necessary BRST conditions for physical states in non-Abelian gauge theories, ensuring equivalence between decoupled and coupled formulations using systematic procedures.

Contribution

It introduces a systematic method to identify which BRST charges must annihilate physical states in decoupled formulations of gauge theories.

Findings

Clarified the role of multiple nilpotent charges in physical state conditions.

Provided a systematic procedure for selecting relevant BRST conditions.

Ensured equivalence between decoupled and original gauge theory formulations.

Abstract

The existence of several nilpotent Noether charges in the decoupled formulation of two-dimensional gauge theories does not imply that all of these are required to annihilate the physical states. We elucidate this matter in the context of simple quantum mechanical and field theoretical models, where the structure of the Hilbert space is known. We provide a systematic procedure for deciding which of the BRST conditions is to be imposed on the physical states in order to ensure the equivalence of the decoupled formulation to the original, coupled one.