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We study the structure of soliton-monopole systems when Fermi fields are present. We show that the existence of a nondegenerate, isolated, zero-energy, c-number solution of the Dirac equation implies that the soliton is a degenerate doublet with Fermi number. We find such solutions in the theory of Yang-Mills monopoles and dyons.
Jackiw et al. (Tue,) studied this question.