Glauber’s coherent states and the semiclassical propagator

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Abstract
This paper studies the classical propagator on Glauber’s coherent states in a generalized P-form. A full class of equivalent expressions labeled by a complex number is found through a direct WKB expansion. The study of matrix elements of the propagator between coherent states shows that they match Klauder’s classical expression but are in some disagreement in the semiclassical order with expression derived through path integral procedures. Arguments are given that favor the present results. The properties of the time propagator with respect to symmetry operations are stated. Possible extensions are briefly discussed.