Communications in Mathematical Physics

, Volume 93, Issue 3, pp 367–378

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


  • David Groisser
    • Mathematical Sciences Research Institute

DOI: 10.1007/BF01258535

Cite this article as:
Groisser, D. Commun.Math. Phys. (1984) 93: 367. doi:10.1007/BF01258535


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-actionL1,loc2 configuration. In particular the result is true for smooth configurations. The monopole number is shown to decompose the configuration space into path components.

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© Springer-Verlag 1984