Charge quantization conditions based on the Atiyah--Singer index theorem
Abstract
Dirac's quantization condition, eg=n/2 (n ∈ Z), and Schwinger's quantization condition, eg=n (n ∈ 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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