Charge quantization conditions based on the Atiyah--Singer index theorem

Details Charge quantization conditions based on the Atiyah--Singer index theorem Charge quantization conditions based on the Atiyah--Singer index theorem

2005-12-06

arxiv.org/abs/hep-th/0512063v3

Prog.Theor.Phys.115:1137-1149,2006

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, no figures; minor corrections, references added, published version

Scientific paper

10.1143/PTP.115.1137

Dirac's quantization condition, $eg=n/2$ ($n \in \Bbb Z$), and Schwinger's quantization condition, $eg=n$ ($n \in \Bbb Z$), for an electric charge $e$ and a magnetic charge $g$ are derived by utilizing the Atiyah-Singer index theorem in two dimensions. The massless Dirac equation on a sphere with a magnetic-monopole background is solved in order to count the number of zero-modes of the Dirac operator.

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