The classical dynamic symmetry for the Sp(1)-kepler problems

Sofiane Bouarroudj, Guowu Meng

Research output: Contribution to journalArticle

Abstract

A Poisson realization of the simple real Lie algebra so*(4n) on the phase space of each Sp(1)-Kepler problem is exhibited. As a consequence, one obtains the Laplace-Runge- Lenz vector for each classical Sp(1)-Kepler problem. The verification of these Poisson realizations is greatly simplified via an idea ofWeinstein. The totality of these Poisson realizations is shown to be equivalent to the canonical Poisson realization of so*(4n) on the Poisson manifold T*H* n/Sp(1). (Here H* n:= Hn\(0) and the Hamiltonian action of Sp(1) on T*H* n is induced from the natural right action of Sp(1) on H* n.) Published by AIP Publishing.

Original languageEnglish (US)
Article number1.5001688
JournalJournal of Mathematical Physics
Volume58
Issue number9
DOIs
StatePublished - Sep 1 2017

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Kepler
Siméon Denis Poisson
algebra
Symmetry
symmetry
Hamiltonian Actions
Poisson Manifolds
Laplace
Phase Space
Lie Algebra

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The classical dynamic symmetry for the Sp(1)-kepler problems. / Bouarroudj, Sofiane; Meng, Guowu.

In: Journal of Mathematical Physics, Vol. 58, No. 9, 1.5001688, 01.09.2017.

Research output: Contribution to journalArticle

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