Path integral for coherent states of the dynamical group SU(1,1)

Abstract

Path integrals over coherent states of the dynamical group (noninvariance group) SU(1,1) are constructed. From the continuous limit the relevant classical dynamics is extracted and is shown to take place in a curved phase space of the form of a Lobachevskii plane. Applications are made to the harmonic oscillator, a model of superfluid helium, the Morse oscillator, and the hydrogen atom. It is shown that when SU(1,1) is the relevant dynamical group the motion will appear oscillator-like on the Lobachevskii plane.