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

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