BRST Formulation of Partition Function Constraints

TL;DR

This paper develops a BRST-based framework for formulating and analyzing constraints on the generating functional in quantum field theory, introducing higher-order nilpotent operators and a master equation for the free energy.

Contribution

It introduces a novel BRST extension approach for generating functional constraints using nilpotent operators of arbitrary order and a master equation involving higher antibrackets.

Findings

Establishes a connection between constraints and BRST-extensions.

Defines a tower of higher antibrackets for the master equation.

Provides a formalism for analyzing free energy with external sources.

Abstract

We show that constraints on the generating functional have direct BRST-extensions in terms of nilpotent operators $\Delta$ that annihilate this generating functional, and which may be of arbitrarily high order. The free energy $F$ in the presence of external sources thus satisfies a ``Master Equation'' which is described in terms of a tower of higher antibrackets.