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.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics