Quantization of a generally covariant gauge system with two super Hamiltonian constraints

TL;DR

This paper develops a BRST operator quantization method for a finite-dimensional gauge system with two super Hamiltonian constraints, modeling the algebra of General Relativity to enable consistent quantization.

Contribution

It introduces a Hermitian nilpotent BRST generator for a model with constraints mimicking General Relativity, providing a new approach to quantizing such systems.

Findings

Successfully constructs a Hermitian nilpotent BRST operator

Defines a physical inner product for the model

Models the constraint algebra of General Relativity

Abstract

The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a finite-dimensional gauge system featuring two quadratic super Hamiltonian and m linear supermomentum constraints is studied as a model for quantizing generally covariant gauge theories. The proposed model ``completely'' mimics the constraint algebra of General Relativity. The Dirac constraint operators are identified by realizing the BRST generator of the system as a Hermitian nilpotent operator, and a physical inner product is introduced to complete a consistent quantization procedure.