Gauge covariant algebras and local BRST cohomology

TL;DR

This paper reviews the formulation of local BRST cohomology on infinite jet bundles, its relation to gauge covariant algebras, and illustrates the concepts through geodesic motion in Riemannian manifolds, highlighting symmetries and deformations.

Contribution

It provides a comprehensive review of local BRST cohomology and demonstrates its application to geodesic motion, connecting gauge covariant algebras with physical symmetries.

Findings

Computed BRST cohomology for geodesic motion

Identified symmetries and constants of motion

Discussed consistent deformations

Abstract

The formulation of the local BRST cohomology on infinite jet bundles and its relation and reduction to gauge covariant algebras are reviewed. As an illustration, we compute the local BRST cohomology for geodesic motion in (pseudo-) Riemannian manifolds and discuss briefly the result (symmetries, constants of the motion, consistent deformations).