On Kählerian coherent states. (English) Zbl 0979.53096

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1-10, 1999. Sofia: Coral Press Scientific Publishing. 241-256 (2000).
Summary: A reformulation of Rawnsley’s Kählerian coherent states (in the framework of geometric quantization) is used in order to investigate the interplay between their local and global properties (projective embeddings) and the relationship with Klauder quantization (via path integrals and the introduction of a metric on the classical phase space). A Klauder type formula is established for the projection operator onto the quantum Hilbert space (the kernel of a Bochner Laplacian) in terms of a phase space path integral. As a further application, a Riemann surface diastatic identity is derived, yielding, via Green function theory, a short proof of the Abel-Jacobi theorem (and conversely), together with some coherent state induced theta function identities.
For the entire collection see [Zbl 0940.00039].


53D50 Geometric quantization
81R30 Coherent states
81S10 Geometry and quantization, symplectic methods
81S40 Path integrals in quantum mechanics
14H42 Theta functions and curves; Schottky problem