On Kählerian coherent states. (English) Zbl 0979.53096

Spera, Mauro

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].

MSC:

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

Keywords:

Kählerian coherent states; Klauder quantization; projection operator; Bochner Laplacian; phase space path integral