Correspondence Rules for SU(1,1) Quasidistribution Functions and Quantum Dynamics in the Hyperbolic Phase Space

Abstract

We derive the explicit differential form for the action of the generators of the SU(1,1) group on the corresponding s-parametrized symbols. This allows us to obtain evolution equations for the phase-space functions on the upper sheet of the two-sheet hyperboloid and analyze their semiclassical limits. Dynamics of quantum systems with SU(1,1) symmetry governed by compact and non-compact Hamiltonians are discussed in both quantum and semiclassical regimes.