, 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.

Research supported in part by NSF Grants 8120790 and PHY-03669
Communicated by A. Jaffe