On the geometry of the Batalin-Vilkovisky Laplacian

TL;DR

This paper introduces a jet-space analog of the BV-Laplacian that avoids delta-functions and infinite constants, revealing that its properties stem from jet-space geometry, thus providing a new geometric perspective on BV formalism.

Contribution

It develops a jet-space based version of the BV-Laplacian, clarifying its geometric foundations and eliminating traditional analytical complications.

Findings

The jet-space analog reproduces key properties of the BV-Laplacian.

Main properties originate from jet-space geometry, not delta-functions.

Provides a geometric understanding of the BV-Laplacian and Schouten bracket.

Abstract

We define a jet-space analog of the BV-Laplacian, avoiding delta-functions and infinite constants; instead we show that the main properties of the BV-Laplacian and its relation to the Schouten bracket originate from the underlying jet-space geometry.