MONOPOLE VECTOR SPHERICAL-HARMONICS

Eigenfunctions of total angular momentum for a charged vector field in teracting with a magnetic monopole are constructed and their propertie s studied. In general, these eigenfunctions can be obtained by applyin g vector operators to the monopole spherical harmonics in a manner sim ilar to that often used for the construction of the ordinary vector sp herical harmonics. This construction fails for the harmonics with the minimum allowed angular momentum. These latter form a set of vector fi elds with vanishing covariant curl and covariant divergence, whose num ber can be determined by an index theorem.