Exclusion of a dyon solution

We prove the nonexistence of finite-energy Julia-Zee dyon solutions, in the Bogomol'ny-Prosad-Sommerfield limit, and the generalizations to SU(N) gauge groups, with the same asymptotic value for the Higgs field and the time component of the gauge field. This gives a physically relevant example showing how the topological arguments can fail to provide the existence of a solution in the presence of a nontrivial topological charge