Dirac prescription from BRST symmetry in FRW space-time

TL;DR

This paper develops a method to derive the BRST charge in extended phase space for FRW space-time, enabling consistent quantization and the recovery of classical observables within a cohomological framework.

Contribution

It introduces a procedure to define the BRST charge from the Noether charge in extended phase space for FRW models, linking gauge fixing, cohomology, and quantization.

Findings

Successfully reproduces known results in FRW space-time

Defines a scalar product implementing the superHamiltonian constraint

Clarifies the cohomological structure of classical observables

Abstract

A procedure to define the BRST charge from the Noether one in extended phase space is given. It is outlined how this prescription can be applied to a Friedmann-Robertson-Walker space-time with a differential gauge condition and it allows us to reproduce the results of [19]. Then we discuss the cohomological classes associated with functions in extended phase space having ghost number one and we recover the frozen formalism for classical observables. Finally, we consider the quantization of BRST-closed states and we define a scalar product which implements the superHamiltonian constraint.