A superintegrable time-dependent system with Kac-Moody symmetry

J. Daboul; P. Winternitz

doi:10.1134/1.1490099

A superintegrable time-dependent system with Kac-Moody symmetry

J. Daboul, P. Winternitz

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the Hamiltonian H_KL with a time-dependent potential in N-dimensional space that is a special combination of a Kepler and a harmonic-oscillator potential. The corresponding classical system has an angular-momentum tensor and a time-dependent analog of the Laplace-Runge-Lenz vector, which commute with the "quasi-Hamiltonian" H_c. These quantities are conserved on the orbits of H_KL, and their Poisson brackets yield a realization of twisted or untwisted centerless Kac-Moody algebras of so(N + 1). The corresponding quantum-mechanical operators and their commutators yield a representation of the positive subalgebras of the above Kac-Moody algebras.

Original language	English
Pages (from-to)	1000-1007
Number of pages	8
Journal	Physics of Atomic Nuclei
Volume	65
Issue number	6
DOIs	https://doi.org/10.1134/1.1490099
State	Published - 1 Jan 2002
Externally published	Yes

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Nuclear and High Energy Physics

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author = "J. Daboul and P. Winternitz",

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N2 - We investigate the Hamiltonian HKL with a time-dependent potential in N-dimensional space that is a special combination of a Kepler and a harmonic-oscillator potential. The corresponding classical system has an angular-momentum tensor and a time-dependent analog of the Laplace-Runge-Lenz vector, which commute with the "quasi-Hamiltonian" Hc. These quantities are conserved on the orbits of HKL, and their Poisson brackets yield a realization of twisted or untwisted centerless Kac-Moody algebras of so(N + 1). The corresponding quantum-mechanical operators and their commutators yield a representation of the positive subalgebras of the above Kac-Moody algebras.

AB - We investigate the Hamiltonian HKL with a time-dependent potential in N-dimensional space that is a special combination of a Kepler and a harmonic-oscillator potential. The corresponding classical system has an angular-momentum tensor and a time-dependent analog of the Laplace-Runge-Lenz vector, which commute with the "quasi-Hamiltonian" Hc. These quantities are conserved on the orbits of HKL, and their Poisson brackets yield a realization of twisted or untwisted centerless Kac-Moody algebras of so(N + 1). The corresponding quantum-mechanical operators and their commutators yield a representation of the positive subalgebras of the above Kac-Moody algebras.

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A superintegrable time-dependent system with Kac-Moody symmetry

Abstract

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