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

@article{Schlichenmaier2010BerezinToeplitzQF,
  title={Berezin-Toeplitz Quantization for Compact K{\"a}hler Manifolds. A Review of Results},
  author={Martin Schlichenmaier},
  journal={Advances in Mathematical Physics},
  year={2010},
  volume={2010},
  pages={643-680}
}
This article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kahler 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. 

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