Removability of a codimension four singular set for solutions of a yang mills higgs equation with small energy

We develop a new method for proving regularity for small energy stationary solutions of coupled gauge field equations. Our results duplicate those of Tian--Tao [7] for the pure Yang Mills equations, but our proof is simpler, and obtains bounded curvature without the use of Coulomb gauges. It relies instead on the Weitzenblock formulae, and an improved Kato inequality.