On the Cohomological Derivation of Yang-Mills Theory in the Antifield Formalism

TL;DR

This paper reviews the cohomological approach to deriving Yang-Mills interactions using the antifield formalism, highlighting the order at which deformations are consistent and the obstructions encountered.

Contribution

It provides a cohomological derivation of Yang-Mills theory via BRST deformations, emphasizing the limitations at higher orders due to non-local interactions.

Findings

Coupling deformations stop at second order.

Higher order deformations are obstructed by non-local interactions.

The antifield formalism successfully derives the interacting theory.

Abstract

We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield formalism through several order BRST deformations of the master equation. It is found that the coupling deformations halt exclusively at the second order, whereas higher order deformations are obstructed due to non-local interactions. The results demonstrate the BRST cohomological derivation of the interacting Yang-Mills theory.