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2014 The Universal Kepler Problem
Guowu Meng
J. Geom. Symmetry Phys. 36: 47-57 (2014). DOI: 10.7546/jgsp-36-2014-47-57

Abstract

For each simple euclidean Jordan algebra $V\!,$ we introduce the analogue of hamiltonian, angular momentum and Laplace-Runge-Lenz vector in the Kepler problem. Being referred to as the universal hamiltonian, universal angular momentum and universal Laplace-Runge-Lenz vector respectively, they are elements in (essentially) the TKK (Tits-Kantor-Koecher) algebra of $V$ and satisfy commutation relations similar to the ones for the hamiltonian, angular momentum and Laplace-Runge-Lenz vector in the Kepler problem. We also give some examples of Poisson realization of the TKK algebra, along with the resulting classical generalized Kepler problems. For the simplest simple euclidean Jordan algebra (i.e., $\mathbb R$), we give examples of operator realization for the TKK algebra, along with the resulting quantum generalized Kepler problems.

Citation

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Guowu Meng. "The Universal Kepler Problem." J. Geom. Symmetry Phys. 36 47 - 57, 2014. https://doi.org/10.7546/jgsp-36-2014-47-57

Information

Published: 2014
First available in Project Euclid: 27 May 2017

zbMATH: 1353.70041
MathSciNet: MR3379441
Digital Object Identifier: 10.7546/jgsp-36-2014-47-57

Rights: Copyright © 2014 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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