Berezin-Toeplitz Quantization of compact Kaehler manifolds

Abstract

Invited lecture at the XIV-th workshop on geometric methods in physics, Bialowieza, Poland, July 9-15, 1995. In this lecture results are reviewed obtained by the author together with Martin Bordemann and Eckhard Meinrenken on the Berezin-Toeplitz quantization of compact Kaehler manifolds. Using global Toeplitz operators, approximation results for the quantum operators are shown. From them it follows that the quantum operators have the correct classical limit. A star product deformation of the Poisson algebra is constructed.

Amstex 2.1, 15 pages, minor changes, some annoying typos removed and 2 references added

References in corpus (1)

• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$

Cited by in corpus (7)

• C*-algebraic quantum Gromov-Hausdorff distance
• Asymptotic properties of the Hitchin-Witten connection
• On Gammelgaard's formula for a star product with separation of variables
• Quantum moment map and obstructions to the existence of closed Fedosov star products
• Toeplitz Operators, Kähler Manifolds, and Line Bundles
• Deformation quantization with separation of variables of an endomorphism bundle
• The formal moment map geometry of the space of symplectic connections