BRST quantization of gauge theories like SL(2,R) on inner product spaces

TL;DR

This paper develops general formulas for BRST quantization of finite-dimensional bosonic gauge theories on inner product spaces, with detailed analysis of SL(2,R) models and nonunimodular gauge groups.

Contribution

It introduces new formulas for BRST solutions in inner product spaces and provides explicit analysis of SL(2,R) and nonunimodular gauge group models.

Findings

Derived general solutions for BRST quantization on inner product spaces.

Analyzed SL(2,R) invariant models and geometries of Lagrange multipliers.

Studied gauge models with nonunimodular gauge groups.

Abstract

Some general formulas are derived for the solutions of a BRST quantization on inner product spaces of finite dimensional bosonic gauge theories invariant under arbitrary Lie groups. A detailed analysis is then performed of SL(2,R) invariant models and some possible geometries of the Lagrange multipliers are derived together with explicit results for a class of SL(2,R) models. Gauge models invariant under a nonunimodular gauge group are also studied in some detail.