BRST cohomology of systems with secondary constraints

TL;DR

This paper develops a systematic method to construct the BRST operator for systems with secondary constraints by extending phase space and utilizing symplectic actions related to time translation.

Contribution

It introduces a novel approach to derive the BRST operator from first principles for systems with secondary constraints through phase space extension.

Findings

Constructed BRST operator from first principles

Extended phase space includes time and energy variables

Provides a symplectic framework for secondary constraints

Abstract

Extending phase space to include time and it canonical conjugate energy as well as the usual momentum and position variables, and then introducing the constraint which sets energy equal to the Hamiltonian, gives a symplectic action of the additive group R which corresponds to time translation along the solutions to the equations of motion. This allows the BRST operator of a system with secondary constraints to be constructed from first principles.