BRST operator quantization of generally covariant gauge systems

TL;DR

This paper develops a Hermitian nilpotent BRST operator for a finite-dimensional covariant gauge system, emphasizing the importance of potential inclusion in the kinetic term for consistent scaling invariance, challenging previous curvature-based approaches.

Contribution

It introduces a novel BRST quantization method that naturally incorporates the potential into the kinetic term, ensuring scale invariance without relying on curvature terms.

Findings

The BRST operator is Hermitian and nilpotent for the system.

Potential must enter the kinetic term for scale invariance.

The approach aligns with Jacobi's principle.

Abstract

The BRST generator is realized as a Hermitian nilpotent operator for a finite-dimensional gauge system featuring a quadratic super-Hamiltonian and linear supermomentum constraints. As a result, the emerging ordering for the Hamiltonian constraint is not trivial, because the potential must enter the kinetic term in order to obtain a quantization invariant under scaling. Namely, BRST quantization does not lead to the curvature term used in the literature as a means to get that invariance. The inclusion of the potential in the kinetic term, far from being unnatural, is beautifully justified in light of the Jacobi's principle.