The coupled Yang-Mills-Dirac equations for differential forms (Q1113480)

A version of the coupled Yang-Mills-Dirac equations for differential forms is presented. In this version the equations are defined and conformal in any odd dimension; they share many of the analytic properties of the Yang-Mills-Higgs equations in these dimensions. A point singularity problem is formulated and solved for the Yang-Mills-Dirac equations in dimension 3. In this dimension the solutions can be associated with a nonnegative energy functional resembling the magnetic monopole energy.