Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization

摘要

For arbitrary compact quantizable Kahler manifolds it is shown how a natural formal deformation quantization (star-product) can be obtained via Berezin-Toeplitz operators. Results on their semi-classical behaviour (their asymptotic expansion) due to Bordemann, Meinrenken, and Schlichenmaier are used in an essential manner. It is shown that the star-product is null on constants and fulfills parity. A trace is constructed and the relation to deformation quantization by geometric quantization is given.