Path Integral and Solutions of the Constraint Equations: The Case of Reducible Gauge Theories

TL;DR

This paper demonstrates that the BRST path integral for reducible gauge theories, with proper boundary conditions, solves the constraint equations by linking it to the physical evolution kernel.

Contribution

It establishes a connection between the BRST path integral and the solution of constraint equations in reducible gauge theories, clarifying their relationship.

Findings

BRST path integral solves the constraint equations.

Proper boundary conditions on ghosts are essential.

Connection to the physical evolution kernel is established.

Abstract

It is shown that the BRST path integral for reducible gauge theories, with appropriate boundary conditions on the ghosts, is a solution of the constraint equations. This is done by relating the BRST path integral to the kernel of the evolution operator projected on the physical subspace.