BerezinToeplitz quantization for compact Kaehler manifolds. A Review of Results
Abstract
This article is a review on BerezinToeplitz operator and BerezinToeplitz deformation quantization for compact quantizable Kaehler manifolds. The basic objects, concepts, and results are given. This concerns the correct semiclassical limit behaviour of the operator quantization, the unique BerezinToeplitz deformation quantization (star product), covariant and contravariant Berezin symbols, and Berezin transform. Other related objects and constructions are also discussed.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.2523
 Bibcode:
 2010arXiv1003.2523S
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables;
 58F06 (Primary);
 53D55;
 58G15 (Secondary);
 53C55;
 32C17;
 81S10
 EPrint:
 32 pages