Open Access
VOL. 17 | 2016 Generalized Kepler Problems and Euclidean Jordan Algebras
Guowu Meng

Editor(s) Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka

Geom. Integrability & Quantization, 2016: 72-94 (2016) DOI: 10.7546/giq-17-2016-72-94


This article is a written version of author's lecture on generalized Kepler problems at the XVII-th International Conference on Geometry, Integrability and Quantization, June 5-10, 2015 Varna, Bulgaria. It begins with a review of the Kepler problem for planetary motion and its magnetized cousins, from which a surprising relationship with Lorentz transformation emerges. Next, we give a review for euclidean Jordan algebra and the associated universal Kepler problem. Finally, we demonstrate that, via the universal Kepler problem, a suitable Poisson realization of the conformal algebra for a simple euclidean Jordan algebra gives rise to a super integrable model that resembles the Kepler problem. In particular we demonstrate how the Kepler problem and its magnetized cousins are obtained this way.


Published: 1 January 2016
First available in Project Euclid: 15 December 2015

zbMATH: 1353.70042
MathSciNet: MR3445425

Digital Object Identifier: 10.7546/giq-17-2016-72-94

Rights: Copyright © 2016 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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