Denis V. Juriev
On the Dynamics of Noncanonically Coupled Oscillators and its Hidden Superstructure
Preprint series: ESI preprints

MSC:

58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}

81Q60 Supersymmetric quantum mechanics

Abstract: The classical and quantum dynamics of noncanonically coupled
oscillators is considered. It is shown that though the classical
dynamics is well--defined for both harmonic and anharmonic
oscillators, the quantum one is well--defined in a harmonic case,
admits a hidden (super)hamiltonian formulation, and thus, preserves
the initial operator relations, whereas a na\"\i ve quantization of the
anharmonic case meets with principal difficulties.

Keywords: Classical and quantum dynamics, hamiltonian systems, nonhamiltonian interaction, Lie superalgebras