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arXiv · hep-th/0512063

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

Shinichi Deguchi·Kaoru Kitsukawa
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Abstract

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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Shinichi Deguchi, Kaoru Kitsukawa. 2006-06-21. Charge quantization conditions based on the Atiyah--Singer index theorem. https://doi.org/10.1143/ptp.115.1137

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