Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs system and derivation of a charge quantization condition
High Energy Physics - Theory
2009-03-19 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0705.3161,
title = {Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs system and derivation of a charge quantization condition},
author = {Shinichi Deguchi},
journal= {arXiv preprint arXiv:0705.3161},
year = {2009}
}
Comments
18pages, no figures, minor corrections, published version