Renormalization of gauge invariant operators and anomalies in Yang-Mills theory

Abstract

A long-standing conjecture on the structure of renormalized, gauge invariant, integrated operators of arbitrary dimension in Yang-Mills theory is established. The general solution of the consistency condition for anomalies with sources included is also derived. This is achieved by computing explicitly the cohomology of the full unrestricted Becchi-Rouet-Stora-Tyutin operator in the space of local polynomial functionals with ghost number equal to zero or one. The argument does not use power counting and is purely cohomological. It relies crucially on standard properties of the antifeld formalism.