Partial waves for the linearized Yang–Mills equation about a monopole background

Abstract

The properties of the monopole-vector spherical harmonics that are needed to transform covariant differential equations on charged vector fields in the presence of a monopole into purely radial ones are computed. This further extends the work of Wu and Yang [Nucl. Phys. B 107, 365 (1976)]. As an application, the complete set of partial waves of SU(2) Yang–Mills fluctuations about the U(1) monopole configuration are explicitly computed. They are generated from the scalar solutions to the covariant Laplacian by the covariant operators D and r×D, in analogy with the uncharged case.