Time evolution in general gauge theories defined on inner product spaces

TL;DR

This paper explores how time evolution in general gauge theories on inner product spaces can be understood through BRST singlet states, including cases with explicit time dependence in constraints and Hamiltonians.

Contribution

It demonstrates that time evolution is governed by BRST singlet states in reparametrization invariant theories, extending to cases with explicit time dependence.

Findings

Time evolution linked to BRST singlet states.

Applicable to theories with explicit time-dependent constraints.

Provides a framework for reparametrization invariant gauge theories.

Abstract

As previously shown BRST singlets |s> in a BRST quantization of general gauge theories on inner product spaces may be represented in the form |s>=e^{[Q, \psi]} |\phi> where |\phi> is either a trivially BRST invariant state which only depends on the matter variables, or a solution of a Dirac quantization. \psi is a corresponding fermionic gauge fixing operator. In this paper it is shown that the time evolution is determined by the singlet states of the corresponding reparametrization invariant theory. The general case when the constraints and Hamiltonians may have explicit time dependence is treated.