Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs System and Derivation of a Charge Quantization Condition(Particles and Fields)

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概要

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• 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∈Z), 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.

• 2007-10-25

著者

• DEGUCHI Shinichi

  Institute of Quantum Science, College of Science and Technology, Nihon University

• Deguchi Shinichi

  Institute Of Quantum Science College Of Science And Technology Nihon University

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