A superintegrable time-dependent system with Kac-Moody symmetry

J. Daboul, P. Winternitz

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1000-1007
Number of pages8
JournalPhysics of Atomic Nuclei
Volume65
Issue number6
DOIs
StatePublished - 1 Jan 2002
Externally publishedYes

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