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

Shinichi Deguchi, Kaoru Kitsukawa

Dirac's quantization condition, $eg=n/2$ ($n\in \mathbb{Z}$), and Schwinger's quantization condition, $eg=n$ ($n\in \mathbb{Z}$), for an electric charge $e$ and a magnetic charge $g$ are…