A mild source for the Wu–Yang magnetic monopole

Abstract

Listen

Translate article

We establish that the Wu–Yang monopole needs the introduction of a magnetic point source at the origin in order for it to be a solution of the differential and integral equations for the Yang–Mills theory. That result is corroborated by the analysis through distribution theory, of the two types of magnetic fields relevant for the local and global properties of the Wu–Yang solution. The subtlety lies in the fact that with the non-vanishing magnetic point source required by the Yang–Mills integral equations, the Wu–Yang monopole configuration does not violate, in the sense of distribution theory, the differential Bianchi identity.