, Volume 93, Issue 3, pp 367-378

Integrality of the monopole number in SU(2) Yang-Mills-Higgs theory on ℝ3

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Abstract

We prove that in classical SU(2) Yang-Mills-Higgs theories on ℝ3 with a Higgs field in the adjoint representation, an integer-valued monopole number (magnetic charge) is canonically defined for any finite-actionL 1,loc 2 configuration. In particular the result is true for smooth configurations. The monopole number is shown to decompose the configuration space into path components.