Antibracket, Antifields and Gauge-Theory Quantization

TL;DR

The paper provides a comprehensive review of the Batalin-Vilkovisky antibracket (field-antifield) formalism for gauge theories, clarifying how the classical master equation $(S,S)=0$ encodes the full gauge structure and how antifields function as BRST sources. It systematizes the construction of proper actions and the BRST symmetry, then extends to the quantum master equation and issues of anomalies, regularization, and renormalization. Through eight representative gauge theories, it demonstrates the practical realization of gauge structure, proper solutions, and the gauge-fixing procedure via the fermionic functional $\Psi$, including delta-function and gaussian gauge-fixing, non-minimal sectors, and gauge-fixed BRST transformations. The work also discusses the relation between different field bases, canonical transformations, and the gauge-fixed basis, highlighting both the strengths (covariant quantization, manifest BRST symmetry) and challenges (measure, anomalies, and open algebras) of the formalism. Collectively, the article provides a self-contained framework for covariant quantization of general gauge systems, with explicit constructions applicable to string theory and higher-form gauge theories.

Abstract

The antibracket formalism for gauge theories, at both the classical and quantum level, is reviewed. Gauge transformations and the associated gauge structure are analyzed in detail. The basic concepts involved in the antibracket formalism are elucidated. Gauge-fixing, quantum effects, and anomalies within the field-antifield formalism are developed. The concepts, issues and constructions are illustrated using eight gauge-theory models.