Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization
量子代数
2007-05-23 v1 数学物理
复变函数
微分几何
math.MP
量子物理
摘要
For arbitrary compact quantizable Kaehler 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.
引用
@article{arxiv.math/9910137,
title = {Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization},
author = {Martin Schlichenmaier},
journal= {arXiv preprint arXiv:math/9910137},
year = {2007}
}
备注
Amslatex, 18 pages