A comparison of definitions for the Schouten bracket on jet spaces

TL;DR

This paper compares various definitions of the Schouten bracket on jet spaces, analyzing their equivalences and differences, and relating them to the classical case on manifolds, to clarify their roles in Poisson and BV formalisms.

Contribution

It provides a systematic comparison of different Schouten bracket definitions on jet spaces and clarifies their relationships and differences from the classical manifold case.

Findings

Identifies key similarities and differences among definitions

Clarifies how definitions relate to classical manifold case

Provides insights into the role of the Schouten bracket in gauge theories

Abstract

The Schouten bracket (or antibracket) plays a central role in the Poisson formalism and the Batalin-Vilkovisky quantization of gauge systems. There are several (in)equivalent ways to realize this concept on jet spaces. In this paper, we compare the definitions, examining in what ways they agree or disagree and how they relate to the case of usual manifolds.