Bianchi identities for yang-mills fields

Abstract

We propose an indirect way to study some solutions of Yang-Mills equations, which is based on the analysis of the following closely related equations: F+A×F=0 and F»+A×F»=0. The former is one of the standard Yang-Mills equations. The latter is the well- known "Bianchi identity" for Yang-Mills fields; but here we do not assume the usual relation between field strenghts and potentials of the Yang-Mills equations. We give a method that allows the investigation of certain families of solutions of these equations. In particular, we find a family of solutions that does not contain any solution of the Yang-Mills equations. The inverse, of course, cannot happen