BRST Reduction of Quantum Algebras with $^*$-Involutions

TL;DR

This paper explores how the BRST reduction procedure interacts with Hermiticity in quantum algebras, establishing conditions under which the reduction preserves the Hermitian structure for compact Lie groups.

Contribution

It introduces a generalized framework for BRST algebras with involutions and demonstrates the compatibility of quantum BRST reduction with Hermiticity for compact Lie groups.

Findings

Quantum BRST quotient and cohomology are isomorphic in zero degree for compact Lie groups.

Reduction preserves Hermiticity under the established framework.

New BRST quotients are obtained via adjoint BRST differentials.

Abstract

In this paper we investigate the compatibility of the BRST reduction procedure with the Hermiticity of star products. First, we introduce the generalized notion of abstract BRST algebras with corresponding involutions. In this setting we define adjoint BRST differentials and as a consequence one gets new BRST quotients. Passing to the quantum BRST setting we show that for compact Lie groups the new quantum BRST quotient and the quantum BRST cohomology are isomorphic in zero degree implying that reduction is compatible with Hermiticity.