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Prog. Theor. Phys. Vol. 115 No. 6 (2006) pp. 1137-1149
Charge Quantization Conditions Based on the Atiyah-Singer Index Theorem
Shinichi Deguchi1,* and
Kaoru Kitsukawa2,**
1Institute of Quantum Science, College of Science and Technology,
Nihon University, Tokyo 101-8308, Japan
2Graduate School of Quantum Science and Technology,
Nihon University, Tokyo 101-8308, Japan
(Received February 27, 2006)
Abstract:
Dirac's quantization condition, eg = n/2 (n ∈\BbbZ),
and Schwinger's quantization condition, eg = n (n ∈\BbbZ),
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.
URL :
http://ptp.ipap.jp/link?PTP/115/1137/
DOI : 10.1143/PTP.115.1137
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Citing Article(s) :
-
Progress of Theoretical Physics Vol. 118 No. 4 (2007) pp. 769-784
:
-
Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs System and Derivation of a Charge Quantization Condition
-
Shinichi Deguchi
