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Berezin-Toeplitz quantization and naturally defined star products for Kähler manifolds

Berezin-Toeplitz quantization and naturally defined star products for Kähler manifolds For compact quantizable Kähler manifolds the Berezin-Toeplitz quantization schemes, both operator and deformation quantization (star product) are reviewed. The treatment includes Berezin’s covariant symbols and the Berezin transform. The general compact quantizable case was done by Bordemann–Meinrenken–Schlichenmaier, Schlichenmaier, and Karabegov–Schlichenmaier. For star products on Kähler manifolds, separation of variables, or equivalently star product of (anti-) Wick type, is a crucial property. As canonically defined star products the Berezin-Toeplitz, Berezin, and the geometric quantization are treated. It turns out that all three are equivalent, but different. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Berezin-Toeplitz quantization and naturally defined star products for Kähler manifolds

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-018-0225-9
Publisher site
See Article on Publisher Site

Abstract

For compact quantizable Kähler manifolds the Berezin-Toeplitz quantization schemes, both operator and deformation quantization (star product) are reviewed. The treatment includes Berezin’s covariant symbols and the Berezin transform. The general compact quantizable case was done by Bordemann–Meinrenken–Schlichenmaier, Schlichenmaier, and Karabegov–Schlichenmaier. For star products on Kähler manifolds, separation of variables, or equivalently star product of (anti-) Wick type, is a crucial property. As canonically defined star products the Berezin-Toeplitz, Berezin, and the geometric quantization are treated. It turns out that all three are equivalent, but different.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Apr 12, 2018

References