SU(1, 1) coherence-preserving Hamiltonians: a path-integral approach

G. Kordas, Dimitrios Kalantzis, A. I. Karanikas

Christopher C. Gerry

We use SU(1,1) coherent-state path integrals to describe the time evolution of systems driven by coherence-preserving Hamiltonians. Such Hamiltonians are composed of linear combinations of the group generators. The method described here is an alternative to the well-known Wei-Norman procedures. Application is made to the degenerate parametric amplifier of quantum optics.

Christopher C. Gerry

Kazuyuki Fujii, Kunio Funahashi

We extend the Barut–Girardello coherent state for the representation of SU(1,1) to the coherent state for a representation of U(N,1) and construct the measure. We also construct a path integral formula for some Hamiltonian.

E. A. Kochetov

A path integral written in terms of the group theoretic coherent states by using the Kähler structure of the coherent state manifold with the particular emphasis on the boundary-fixing term derivation is considered herein. The path integral for a propagator of the system with Hamiltonian linear in the SU(2)/SU(1,1) generators is shown to be diagonalized by an appropriate motion in the phase space.