2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152269The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for the dimension of projective Hilbert space and a simple geometric interpretation of Calabi's diastasis follows.8 pages, Latex2e, ams fonts, to appear in "Quantization, Coherent States and Poisson Structures", Wydawnictwo Naukowe PWN (Warshaw), Edited by A. Strasburger, S. Twareque Ali, J.-P. Antoine and A. Odzijewicz, Proceedings of the XIV Workshop on Geometric Methods in Physics, Białowieża, Poland, 9-15 july 1995.Differential Geometry81R30text