## 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

### MSC:

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

### Keywords:

Yang-Mills-Higgs theories; magnetic charge; monopole number
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### References:

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