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Spectrum of Schroedinger field in a noncommutative magnetic monopole

D. Karabali·V. P. Nair·A. P. Polychronakos
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Abstract

The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged Schroedinger field coupled to a noncommutative U(1) gauge field is identified. It is shown that the Hamiltonian is essentially the angular momentum squared of the particle, but with a nontrivial scaling factor appearing, in agreement with the first-quantized canonical treatment of the problem. Monopole quantization is recovered and identified as the quantization of a commutative Seiberg-Witten mapped monopole field.

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D. Karabali, V. P. Nair, A. P. Polychronakos. 2001-12-11. Spectrum of Schroedinger field in a noncommutative magnetic monopole. https://doi.org/10.1016/s0550-3213(02)00062-7

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