Charge Quantization Conditions Based on the Atiyah-Singer Index Theorem | Zendy

Shinichi Deguchi | Zendy; K Kitsukawa | Zendy

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Charge Quantization Conditions Based on the Atiyah-Singer Index Theorem

Author(s) -

Shinichi Deguchi,

K Kitsukawa

Publication year - 2006

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.115.1137

Subject(s) - physics , magnetic monopole , quantization (signal processing) , atiyah–singer index theorem , mathematical physics , massless particle , dirac operator , dirac equation , canonical quantization , dirac (video compression format) , charge (physics) , quantum electrodynamics , quantum mechanics , quantum , pure mathematics , mathematics , algorithm , quantum gravity , neutrino

Dirac's quantization condition, $eg=n/2$ ($n \in \Bbb Z$), and Schwinger'squantization condition, $eg=n$ ($n \in \Bbb Z$), for an electric charge $e$ anda magnetic charge $g$ are derived by utilizing the Atiyah-Singer index theoremin two dimensions. The massless Dirac equation on a sphere with amagnetic-monopole background is solved in order to count the number ofzero-modes of the Dirac operator.Comment: 16 pages, no figures; minor corrections, references added, published versio

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