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

Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs system and derivation of a charge quantization condition - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

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 theheat kernel method and a nonlinear realization of SU(2) gauge symmetry. Thistheorem is applied to the problem of deriving a charge quantization conditionin the four-dimensional SO(3) YMH system with non-Abelian monopoles. Theresulting quantization condition, eg=n (n: integer), for an electric charge eand a magnetic charge g is consistent with that found by Arafune, Freund andGoebel. It is shown that the integer n is half of the index of a Diracoperator.

Author: ** Shinichi Deguchi**

Source: https://arxiv.org/