Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs system and
  derivation of a charge quantization condition   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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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc