Some new approaches in Berezin-Toeplitz quantization
主 题: Some new approaches in Berezin-Toeplitz quantization
报告人: Professor Miroslav Englis (捷克科学院 数学研究所)
时 间: 2006-10-27 下午 2:30 - 3:30
地 点: 理科一号楼 1114(数学所活动)
The~traditional approach towards quantizing a system with
internal degrees of freedom consists in replacing the original Hilbert
space by its tensor product with a finite-dimensional space carrying
the internal degrees of freedom. We~describe a method that leads to a
Berezin-Toeplitz type quantization which turns out to incorporate not
only the traditional approach mentioned above, but~also the original
degreeless quantization as well as a host of quantum objects that do
not have a semiclassical limit in the usual~sense. The~method is based
on extending the usual Berezin-Toeplitz quantization to reproducing
kernel spaces of matrix-valued functions, which turns out to give
rise to some completely new phenomena.
