Solitons with fermion number ½

Abstract

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 \ifmmode\pm\else\textpm\fi{} \textonehalf{}. We find such solutions in the theory of Yang-Mills monopoles and dyons.