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Removable singularities of coupled Yang-Mills fields in $$R^ 3$$. (English) Zbl 0552.35028
It is proved that a coupled Yang-Mills-Higgs field in $${\mathbb{R}}^ 3$$ with a point singularity is gauge equivalent to a smooth field provided that certain integral norms of the fields are finite. The assumption on the curvature is that it is in $$L^{3/2}$$. The assumption on the Higgs field depends on the sign of a coupling constant $$\lambda$$. If $$\lambda >0$$ there is no restriction but if $$\lambda <0$$ the field is assumed to be in $$L^{3+\epsilon}$$ for some $$\epsilon >0$$. Examples are given to show the necessity of these assumptions. The results and techniques used in this paper complement and extend a previous paper by one of the authors where the pure Yang-Mills case is treated.
Reviewer: M.Min-Oo

##### MSC:
 35J60 Nonlinear elliptic equations 81T08 Constructive quantum field theory
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##### References:
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