BRST-Invariant Constraint Algebra in Terms of Commutators and Quantum Antibrackets

TL;DR

This paper develops a comprehensive algebraic framework for BRST-invariant constraints using commutators and quantum antibrackets, extending phase space and demonstrating equivalence to standard BRST-BFV methods.

Contribution

It introduces a novel formulation of BRST-invariant constraint algebra in extended phase space with explicit gauge algebra forms for rank-one theories.

Findings

Explicit BRST-invariant gauge algebra for rank-one theories

Construction of a gauge-fixed unitarizing Hamiltonian

Formalism shown to be equivalent to standard BRST-BFV approach

Abstract

General structure of BRST-invariant constraint algebra is established, in its commutator and antibracket forms, by means of formulation of algebra-generating equations in yet more extended phase space. New ghost-type variables behave as fields and antifields with respect to quantum antibrackets. Explicit form of BRST-invariant gauge algebra is given in detail for rank-one theories with Weyl- and Wick- ordered ghost sector. A gauge-fixed unitarizing Hamiltonian is constructed, and the formalism is shown to be physically equivalent to the standard BRST-BFV approach.