The Yang--Mills gauge field theory in the context of a generalized BRST--formalism including translations

TL;DR

This paper explores the algebraic renormalization of Yang--Mills gauge theories incorporating translations, revealing a closed algebra that simplifies the derivation of solutions to descent equations.

Contribution

It introduces a generalized BRST formalism including translations, leading to a closed algebra that streamlines the analysis of gauge theories.

Findings

Closed algebra between operators due to translations

Unified parameter formula for descent equations

Simplified derivation of nontrivial solutions

Abstract

We discuss the algebraic renormalization of the Yang--Mills gauge field theory in the presence of translations. Due to the translations the algebra between Sorella's $\d$--operator, the exterior derivative and the BRST--operator closes. Therefore, we are able to derive an integrated parameter formula collecting in an elegant and compact way all nontrivial solutions of the descent equations.