Fermions interacting with spherically symmetric monopoles: Beyond the step-function approximation

Abstract

We analyze the interactions of massless fermions in arbitrary representations of the gauge group, with general spherically symmetric monopoles of arbitrary strength. We obtain the conditions for finiteness of the solutions to the Dirac equation at the origin, evolve it through arbitrary radial functions, and obtain the boundary conditions at the monopole-core radius, thus improving upon the step-function approximation previously used. We show that our results differ from the results using the step-function approximation only when the boundary conditions are not diagonalizable on the physical basis, and hence processes involving such cases may be used to probe the structure of the monopole core.