Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules

Details Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules

2007-02-26

arxiv.org/abs/math-ph/0702086v4

J. Math. Phys. 52, 042106 (2011)

Physics

Mathematical Physics

27 pages, Refs. updated

Scientific paper

For each integer $n\ge 1$, we demonstrate that a $(2n+1)$-dimensional generalized MICZ-Kepler problem has an $\mr{Spin}(2, 2n+2)$ dynamical symmetry which extends the manifest $\mr{Spin}(2n+1)$ symmetry. The Hilbert space of bound states is shown to form a unitary highest weight $\mr{Spin}(2, 2n+2)$-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest weight modules. As a byproduct, we get a simple geometric realization for such a unitary highest weight $\mr{Spin}(2, 2n+2)$-module.

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