On the Geometry of the Batalin-Vilkovisky Formalism

TL;DR

This paper proposes an invariant geometric definition of the BV operator as divergence of Hamiltonian vector fields, explores its properties, and discusses its geometric interpretation with an example on Kähler supermanifolds.

Contribution

It introduces a new invariant geometric definition of the BV operator and analyzes its properties and geometric significance.

Findings

Defined the BV operator as divergence of Hamiltonian vector fields

Analyzed properties of the BV operator derived from this definition

Provided an example realization on Kählerian supermanifolds

Abstract

An invariant definition of the operator $\Delta $ of the Batalin-Vilkovisky formalism is proposed. It is defined as the divergence of a Hamiltonian vector field with an odd Poisson bracket (antibracket). Its main properties, which follow from this definition, as well as an example of realization on K\"ahlerian supermanifolds, are considered. The geometrical meaning of the Batalin-Vilkovisky formalism is discussed.