Basics of BRST quantization on inner product spaces

TL;DR

This paper explores the foundational aspects of BRST quantization on inner product spaces, detailing state representations, gauge fixing, and symmetry properties in both abelian and nonabelian models, with a focus on the role of SL(2,R).

Contribution

It provides a detailed analysis of BRST invariant states, gauge fixing choices, and the application of SL(2,R) symmetry in both abelian and nonabelian models within the operator formalism.

Findings

BRST invariant states can be expressed as e^{[Q,]} |>

SL(2,R) acts as a natural extended gauge symmetry

The approach applies to both abelian and nonabelian models

Abstract

There is an elaborated abstract form of BRST quantization on inner product spaces within the operator formalism which leads to BRST invariant states of the form |ph>=e^{[Q,\psi]} |\phi> where \psi is a gauge fixing fermion, and where |\phi> is a BRST invariant state determined by simple hermitian conditions. These state representations are closely related to the path integral formulation. Here we analyse the basics of this approach in detail. The freedom in the choice of \psi and |\phi> as well as their properties under gauge transformations are explicitly determined for simple abelian models. In all considered cases SL(2,R) is shown both to be a natural extended gauge symmetry and to be useful to determine |ph>. The results are also applied to nonabelian models.