Some exact dyon solutions for the classical Yang-Mills field equation

Abstract

Many exact dyon solutions for the classical Yang-Mills field equation with Higgs scalar fields are obtained in Minkowski space. We accomplish this by solving the field equation for a sourceless Yang-Mills theory using the self-duality condition and a specific ansatz in Euclidean space. Each of our sourceless solutions in SU(2) can be converted into one of the real solutions in $\mathrm{SL}(2, C)$ previously discussed by Wu and Yang.