Berezin-Toeplitz quantization and Berezin symbols for arbitrary compact Kaehler manifolds
Quantum Algebra
2016-09-07 v2 High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Complex Variables
Differential Geometry
math.MP
Symplectic Geometry
Quantum Physics
Abstract
For phase-space manifolds which are compact Kaehler manifolds relations between the Berezin-Toeplitz quantization and the quantization with the help of Berezin's coherent states and symbols are studied. First the results on the Berezin-Toeplitz quantization of arbitrary compact Kaehler manifolds due to Bordemann, Meinrenken and Schlichenmaier are recalled. It is shown that the covariant symbol map is adjoint to the Toeplitz map. The Berezin transform for compact Kaehler manifolds is discussed. (Talk presented at the XVII workshop on geometric methods in physics, Bialowieza, Poland, July 3 --July 9, 1998)
Keywords
Cite
@article{arxiv.math/9902066,
title = {Berezin-Toeplitz quantization and Berezin symbols for arbitrary compact Kaehler manifolds},
author = {Martin Schlichenmaier},
journal= {arXiv preprint arXiv:math/9902066},
year = {2016}
}
Comments
11 pages, Amslatex, some annoying typos removed (missing superscript, or superscripts at the wrong places)