Note on Constrained Cohomology

TL;DR

This paper investigates the cohomology of the BRS operator in gauge-invariant local functionals, introducing a filtration method and applying it to topological Yang-Mills theory to deepen understanding of symmetry structures.

Contribution

It presents a novel filtration-based procedure for analyzing BRS cohomology in gauge theories, with specific application to topological Yang-Mills theory.

Findings

Developed a filtration operator counting symmetry parameters.

Applied the method to Witten's topological Yang-Mills theory.

Enhanced understanding of gauge symmetry cohomology structures.

Abstract

The cohomology of the BRS operator corresponding to a group of rigid symmetries is studied in a space of local field functionals subjected to a condition of gauge invariance. We propose a procedure based on a filtration operator counting the degree in the infinitesimal parameters of the rigid symmetry transformations. An application to Witten's topological Yang-Mills theory is given.