Semicoherent states and the group ISp(2, R)

The properties of two structures arising from a particular subset of the general coherent states of ISp(2, R) are studied. At the quantum level, these states support a Hilbert space of analytic functions in two variables which generalizes the Bargmann-Segal space. At a classical level they generate a symplectic manifold on which a Hamiltonian flow is obtained through dequantization via the time-dependent variational principle. This flow provides an approximate description of the coupled motion of the centre of a wave packet and its covariance matrix in phase space.