Stability and instability of the Wu-Yang solution of the Yang-Mills field equation

Abstract

We investigate small perturbations about the spherically symmetric Wu-Yang solution of the Yang-Mills field equation. We show that small nonspherical perturbations are stable. Because of the singularity of the Wu-Yang solution at the origin, $S$-wave perturbations are not stable. In the case of the Prasad-Sommerfield monopole, we explicitly show that the $S$-wave perturbations of both natural and unnatural parity are stable.