Removable singularities for solutions of coupled Yang-Mills-Dirac equations

Abstract

We prove a removable singularity theorem for solutions of coupled Yang-Mills-Dirac equations on compact four-dimensional manifolds. We show that a field satisfying the coupled equations with a point singularity is gauge equivalent to a smooth field if the energy functional is finite. The hypotheses are very natural. Only conformally invariant conditions are placed on force field and particle field interacting with the force field. It is noticeable that there is no assumption on the derivative of the particle field.