Covariance in the Batalin-Vilkovisky formalism and the Maurer-Cartan equation for curved Lie algebras

TL;DR

This paper explores the covariance of the Batalin-Vilkovisky formalism in classical mechanics through the Maurer-Cartan equation in curved Lie superalgebras, linking it to AKSZ field theories.

Contribution

It introduces a novel framework using curved Lie superalgebras and Maurer-Cartan equations to understand BV covariance and constructs a canonical transformation to relate spinning particle and AKSZ theories.

Findings

Covariance expressed via Maurer-Cartan in curved Lie superalgebras

Construction of a BV canonical transformation

Identification of spinning particle with AKSZ field theory

Abstract

We express covariance of the Batalin-Vilkovisky formalism in classical mechanics by means of the Maurer-Cartan equation in a curved Lie superalgebra, defined using the formal variational calculus and Sullivan's Thom-Whitney construction. We use this framework to construct a Batalin-Vilkovisky canonical transformation identifying the Batalin-Vilkovisky formulation of the spinning particle with an AKSZ field theory.