A mild source for the Wu–Yang magnetic monopole
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.