BRST Symmetry and Cohomology

TL;DR

This paper explores the mathematical structure of gauge theories, focusing on BRST symmetry and cohomology, to identify gauge-invariant actions and potential anomalies in standard gauge theories.

Contribution

It provides a detailed, explicit analysis of the cohomological methods used to determine gauge invariants and anomalies, emphasizing the role of Lie algebra cohomology.

Findings

Classification of gauge-invariant actions

Identification of anomaly candidates

Use of Lie algebra cohomology in gauge theories

Abstract

We present the mathematical considerations which determine all gauge invariant actions and anomaly candidates in gauge theories of standard type such as ordinary or gravitational Yang Mills theories. Starting from elementary concepts of field theory the discussion tries to be explicit and complete, only the cohomology of simple Lie algebras it quoted from the literature.