Deformation Theory and the Batalin-Vilkovisky Master Equation

TL;DR

This paper connects the Batalin-Vilkovisky master equations with deformation theory, showing they serve as integrability conditions for algebraic deformations, thus translating BV formalism into deformation language.

Contribution

It establishes a novel interpretation of BV master equations within the framework of deformation theory, bridging two mathematical approaches.

Findings

BV master equations are integrability conditions for algebra deformations

Classical and quantum BV equations correspond to different deformation types

Provides a new perspective on BV formalism through deformation theory

Abstract

The Batalin-Vilkovisky master equations, both classical and quantum, are precisely the integrability equations for deformations of algebras and differential algebras respectively. This is not a coincidence; the Batalin-Vilkovisky approach is here translated into the language of deformation theory.