Universal Propagator for Group-Related Coherent States

In earlier work universal propagators were introduced for the Heisenberg -Weyl group, the affine group, and the rotation group. By generalizing these constructions we show here that it is possible to introduce a universal propagator for a rather general unitary Lie group. In the context of coherent-state representations, the universal propagator is a single function independent of any particular choice of fiducial vector, which nonetheless, propagates all coherent state Hilbert space representatives correctly.