Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization
Quantum Algebra
2007-05-23 v1 Mathematical Physics
Complex Variables
Differential Geometry
math.MP
Quantum Physics
Abstract
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.
Cite
@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}
}
Comments
Amslatex, 18 pages