2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54514We 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.28 pagesHigh Energy Physics - Theorytext