Odd Invariant Semidensity and Divergence-like Operators on an Odd Symplectic Superspace

TL;DR

This paper introduces a divergence-like operator on an odd symplectic superspace that helps construct an odd invariant semidensity, drawing parallels to mean curvature formulas in Euclidean geometry.

Contribution

It presents a new divergence-like operator invariant under odd vector fields and uses it to explicitly construct an odd invariant semidensity in superspace.

Findings

Defined a divergence-like operator on odd symplectic superspace

Constructed an explicit formula for the odd invariant semidensity

Established a geometric analogy with mean curvature in Euclidean space

Abstract

The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The formula for this semidensity is similar to the formula of the mean curvature of hypersurfaces in Euclidean space.