A note on path integrals and time evolutions in BRST quantization

TL;DR

This paper explores the relationship between operator-based BRST quantization and path integral formulation, revealing how specific quantum rules and boundary conditions connect these approaches.

Contribution

It provides a novel interpretation of path integrals in BRST quantization and clarifies the nontrivial relation between Hamiltonians in the two frameworks.

Findings

Formal solutions lead to an unexpected path integral interpretation

Quantum rules are necessary for exact correspondence in the operator method

Boundary conditions and gauge fixing are precisely connected in the path integral

Abstract

Recent formal solutions of BRST quantization on inner product spaces within the operator method are shown to lead to an unexpected interpretation of the conventional path integral formulation. The relation between the Hamiltonians in the two formulations is nontrivial. For the operator method the correspondence requires certain quantum rules which make the formal solutions exact, and for the path integral the correspondence yields a precise connection between boundary conditions and the choice of gauge fixing.