Delta-Operator on Semidensities and Integral Invariants in the Batalin-Vilkovisky Geometry

TL;DR

This paper defines the Delta-operator on semidensities within odd symplectic superspaces and uses it to construct integral invariants, enhancing the understanding of BV formalism geometry.

Contribution

It introduces a new Delta-operator acting on semidensities and applies it to build integral invariants, clarifying the geometric structure of BV formalism.

Findings

Defined the Delta-operator on semidensities.

Constructed integral invariants in odd symplectic superspaces.

Provided a clearer geometric interpretation of BV formalism.

Abstract

The action of Batalin-Vilkovisky Delta-operator on semidensities in an odd symplectic superspace is defined. This is used for the construction of integral invariants on surfaces embedded in an odd symplectic superspace and for more clear interpretation of the Batalin-Vilkovisky formalism geometry.