Monopole Vector Spherical Harmonics

Abstract

Eigenfunctions of total angular momentum for a charged vector field interacting with a magnetic monopole are constructed and their properties studied. In general, these eigenfunctions can be obtained by applying vector operators to the monopole spherical harmonics in a manner similar to that often used for the construction of the ordinary vector spherical harmonics. This construction fails for the harmonics with the minimum allowed angular momentum. These latter form a set of vector fields with vanishing covariant curl and covariant divergence, whose number can be determined by an index theorem.