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

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.

Corrected throughout, and improvements in exposition of Section 6

Cited by in corpus (4)

• Equivariant Batalin-Vilkovisky formalism
• 4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism
• Batalin-Vilkovisky formality for Chern-Simons theory
• DGLA Dg and BV formalism