Symmetries and the Antibracket: The Batalin-Vilkovisky Method

TL;DR

This paper discusses the Batalin-Vilkovisky (BV) quantization method, exploring its derivation from symmetry principles, generalizations of its structure, and connections to Poisson and Nambu brackets.

Contribution

It provides a new perspective on BV quantization by deriving it from Schwinger-Dyson-BRST symmetry and relating it to generalized brackets.

Findings

Derived BV from Schwinger-Dyson-BRST symmetry.

Proposed generalizations of the BV structure.

Connected the antibracket with Poisson and Nambu brackets.

Abstract

These lectures on the Batalin-Vilkovisky method of quantization were delivered at "VII Mexican School of Particles and Fields", M\'erida, M\'exico, October 30-November 6, 1996. In section II, we study the derivation of BV from Schwinger-Dyson-BRST symmetry; in section III, we consider some generalizations of the BV structure suggested by our approach. In section IV, we present a connection between the Poisson bracket and the antibracket and use it to relate the Nambu bracketc with the generalized $n$-brackets of section III.