Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results

الملخص EN

This article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kähler manifolds.

The basic objects, concepts, and results are given.

This concerns the correct semiclassical limit behaviour of the operator quantization, the unique Berezin-Toeplitz deformation quantization (star product), covariant and contravariant Berezin symbols, and Berezin transform.

Other related objects and constructions are also discussed.