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

    Bouarroudj, Sofiane ; Meng, Guowu. / The classical dynamic symmetry for the Sp(1)-kepler problems. In: Journal of Mathematical Physics. 2017 ; Vol. 58, No. 9.
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