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arXiv · 0705.3161

Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs system and derivation of a charge quantization condition

Shinichi Deguchi
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Abstract

The Atiyah-Singer index theorem is generalized to a two-dimensional SO(3) Yang-Mills-Higgs (YMH) system. The generalized theorem is proven by using the heat kernel method and a nonlinear realization of SU(2) gauge symmetry. This theorem is applied to the problem of deriving a charge quantization condition in the four-dimensional SO(3) YMH system with non-Abelian monopoles. The resulting quantization condition, eg=n (n: integer), for an electric charge e and a magnetic charge g is consistent with that found by Arafune, Freund and Goebel. It is shown that the integer n is half of the index of a Dirac operator.

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Shinichi Deguchi. 2007-11-09. Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs system and derivation of a charge quantization condition. https://doi.org/10.1143/ptp.118.769

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