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

2005/12/31 by Shinichi Deguchi, Kaoru Kitsukawa · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP

paper · pdf · doi:10.1143/ptp.115.1137

published as Prog.Theor.Phys.115:1137-1149,2006 · 16 pages, no figures; minor corrections, references added, published version

arxiv created 2006/06/21 · arxiv updated 2009/12/01

Abstract

Dirac's quantization condition, eg=n/2 (n ∈ \Bbb Z), and Schwinger's quantization condition, eg=n (n ∈ \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.

Cited by

• Schwinger's non-commutative coordinates and duality between helicity and Dirac quantisation conditions