Symmetry and exact dyon solutions for classical Yang–Mills field equations

We show that the generalized electromagnetic field tensor $\mathrm{F̄}$ _μν and the magnetic and electric charges in non‐Abelian gauge theories have little to do with the Higgs scalars and/or the dynamics of the Lagrangian. They are consequences of a symmetry in the theory. We present several exact static dyon solutions to the nonlinear classical field equations in both massless and massive Yang–Mills theories, which possess both electric and magnetic charges. The implications of $\mathrm{F̄}$ _μν are also discussed.