2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53975The BRST transformations for the Yang-Mills gauge fields in the presence of gravity described by Ashtekar variables are obtained by using the so-called Maurer-Cartan horizontality conditions. The BRST cohomology group expressed by the Wess-Zumino consistency condition is solved with the help of an operator $δ$ introduced by S.P. Sorella which in our case has a very simple form and generates, together with the differential $d$ and the BRST operator $s$, a simpler algebra than in the pure Yang-Mills theory. In this way we shall find the Yang-Mills Lagrangians, the Chern-Simons terms and the gauge anomalies.20 pages, report REF.TUW 94-17High Energy Physics - Theorytext