Integrality of the monopole number in SU(2) Yang-Mills-Higgs theory on \({\mathbb{R}}^ 3\). (English) Zbl 0564.58039

The author proves that in classical SU(2) Yang-Mills-Higgs theories on \(R^ 3\) with a Higgs field in the adjoint representation, an integer- valued monopole number (magnetic charge) is canonically defined for any finite-action \(L^ 2_{1,loc}\) configuration. In particular the result is true for smooth configurations. The monopole number is shown to decompose the configuration space into path components.
Reviewer: M.Martellini


58J90 Applications of PDEs on manifolds
81T08 Constructive quantum field theory
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