Generalized MICZ-Kepler problems and unitary highest weight modules

Journal Article · Fri Apr 15 04:00:00 EDT 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3574886· OSTI ID:21501301

Meng, Guowu ^[1]; Ruibin, Zhang ^[2]

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1. Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong)
2. School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006 (Australia)

For each integer n{>=} 1, we demonstrate that a (2n+ 1)-dimensional generalized MICZ-Kepler problem has a Spin(2, 2n+ 2) dynamical symmetry which extends the manifest Spin(2n+ 1) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight Spin(2, 2n+ 2)-module with the minimal positive Gelfand-Kirillov dimension. As a byproduct, we obtain a simple geometric realization for such a unitary highest weight Spin(2, 2n+ 2)-module.

• OSTI ID: 21501301
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 4 Vol. 52; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

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MANY-DIMENSIONAL CALCULATIONS
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MATHEMATICS
PARTICLE PROPERTIES
SPACE
SPIN
SYMMETRY