Reducible Gauge Algebra of BRST-Invariant Constraints

TL;DR

This paper develops a comprehensive formulation of reducible gauge algebras using BRST-invariant constraints, extending previous irreducible cases and establishing a unified algebraic framework with applications to both Abelian and non-Abelian theories.

Contribution

It extends the BRST-invariant constraint approach to reducible gauge algebras and introduces a master equation encoding the extended BRST algebra.

Findings

Formulation of reducible gauge algebra with BRST-invariant constraints

Construction of a unitarizing Hamiltonian respecting dual BRST symmetries

Explicit examples for Abelian and non-Abelian theories at various reducibility stages

Abstract

We show that it is possible to formulate the most general first-class gauge algebra of the operator formalism by only using BRST-invariant constraints. In particular, we extend a previous construction for irreducible gauge algebras to the reducible case. The gauge algebra induces two nilpotent, Grassmann-odd, mutually anticommuting BRST operators that bear structural similarities with BRST/anti-BRST theories but with shifted ghost number assignments. In both cases we show how the extended BRST algebra can be encoded into an operator master equation. A unitarizing Hamiltonian that respects the two BRST symmetries is constructed with the help of a gauge-fixing Boson. Abelian reducible theories are shown explicitly in full detail, while non-Abelian theories are worked out for the lowest reducibility stages and ghost momentum ranks.