Jet Bundles in Quantum Field Theory: The BRST-BV method

TL;DR

This paper explores the geometric interpretation of the Batalin-Vilkovisky antibracket using jet bundle formalism, linking it to the Schouten bracket and BRST cohomology in gauge theories.

Contribution

It provides a detailed geometric framework connecting jet bundles, the BV antibracket, and BRST cohomology, enhancing understanding of gauge fixing in quantum field theory.

Findings

Identifies the BV antibracket as the Schouten bracket of functional multivectors.

Reformulates gauge fixing in jet bundle formalism.

Establishes the cohomology of multivectors as BRST cohomology.

Abstract

The geometric interpretation of the Batalin-Vilkovisky antibracket as the Schouten bracket of functional multivectors is examined in detail. The identification is achieved by the process of repeated contraction of even functional multivectors with fermionic functional 1-forms. The classical master equation may then be considered as a generalisation of the Jacobi identity for Poisson brackets, and the cohomology of a nilpotent even functional multivector is identified with the BRST cohomology. As an example, the BRST-BV formulation of gauge fixing in theories with gauge symmetries is reformulated in the jet bundle formalism. (Hopefully this version will be TeXable)