BRST-antifield Quantization: a Short Review

TL;DR

This paper provides a concise review of the BRST-antifield formalism, explaining its role in systematically quantizing gauge theories while maintaining covariance and addressing anomalies.

Contribution

It offers a clear overview of the BRST-antifield approach, highlighting its systematic procedure for gauge quantization and the role of BRST cohomology in physical observables.

Findings

Explains the BRST invariance and its nilpotency.

Describes the quantum master equation and anomaly emergence.

Connects BRST cohomology with physical observables.

Abstract

Most of the known models describing the fundamental interactions have a gauge freedom. In the standard path integral, it is necessary to "fix the gauge" in order to avoid integrating over unphysical degrees of freedom. Gauge independence might then become a tricky issue, especially when the structure of the gauge symmetries is intricate. In the modern approach to this question, it is BRST invariance that effectively implements gauge invariance. This set of lectures briefly reviews some key ideas underlying the BRST-antifield formalism, which yields a systematic procedure to path-integrate any type of gauge system, while (usually) manifestly preserving spacetime covariance. The quantized theory possesses a global invariance under the so-called BRST transformation, which is nilpotent of order two. The cohomology of the BRST differential is the central element that controls the physics. Its relationship with the observables is sketched and explained. How anomalies appear in the "quantum master equation" of the antifield formalism is also discussed. These notes are based on lectures given by MH at the 10th Saalburg Summer School on Modern Theoretical Methods from the 30th of August to the 10th of September, 2004 in Wolfersdorf, Germany and were prepared by AF and AM. The exercises which were discussed at the school are also included.