Master Equations for Extended Lagrangian BRST Symmetries

TL;DR

This paper develops an extended Lagrangian formalism for BRST and anti-BRST symmetries, deriving a master equation that unifies gauge fixing and symmetry invariance in quantum field theories.

Contribution

It introduces a BRST--anti-BRST extension of the Batalin-Vilkovisky formalism based on invariance under both symmetries, providing a new algebraic framework for gauge fixing.

Findings

Derived the BRST--anti-BRST master equation.

Unified gauge fixing with extended BRST symmetry.

Connected solutions to earlier algebraic formalisms.

Abstract

Starting from the requirement that a Lagrangian field theory be invariant under both Schwinger-Dyson BRST and Schwinger-Dyson anti-BRST symmetry, we derive the BRST--anti-BRST analogue of the Batalin-Vilkovisky formalism. This is done through standard Lagrangian gauge fixing respecting the extended BRST symmetry. The solutions of the resulting Master Equation and the gauge-fixing procedure for the quantum action can be brought into forms that coincide with those obtained earlier on algebraic grounds by Batalin, Lavrov and Tyutin.