Semiclassical Propagator in the Generalized Coherent-State Representation

A detailed derivation of the semiclassical propagator in the generalized coherent-state representation is performed by applying the saddle-point method to a path integral over the classical phase space. With the purpose of providing greater accessibility and applicability to the developed formalism, a brief review of the generalized concept of coherent states is presented, in which three examples of coherent-state sets are examined, namely, the canonical, spin, and SU(n) bosonic coherent states.