2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185513An algebraic criterion for the vanishing of the beta function for renormalizable quantum field theories is presented. Use is made of the descent equations following from the Wess-Zumino consistency condition. In some cases, these equations relate the fully quantized action to a local gauge invariant polynomial. The vanishing of the anomalous dimension of this polynomial enables us to establish a nonrenormalization theorem for the beta function $β_g$, stating that if the one-loop order contribution vanishes, then $β_g$ will vanish to all orders of perturbation theory. As a by-product, the special case in which $β_g$ is only of one-loop order, without further corrections, is also covered. The examples of the N=2,4 supersymmetric Yang-Mills theories are worked out in detail.1+32 pages, LaTeX2e, typos correctedHigh Energy Physics - Theorytext