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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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