Berezin-Toeplitz Quantization

SCHLICHENMAIER, Martin

doi:10.1016/b978-0-323-95703-8.00053-7

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Berezin-Toeplitz Quantization

SCHLICHENMAIER, Martin

2025 • In Encyclopedia of Mathematical Physics

Peer reviewed

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https://hdl.handle.net/10993/62713

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10.1016/b978-0-323-95703-8.00053-7

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Keywords :

Geometric quantization, deformation quantization, coherent states; Kaehler manifolds

Abstract :

[en] The Berezin-Toeplitz quantization is a geometrically defined method to quantize Kähler manifolds. Its definition and properties are presented. The notion of a quantizable Kähler manifold is introduced. It is related to the existence of a holomorphic quantum line bundle over the manifold. The quantum states are given by the vector space of holomorphic sections of this line bundle. The quantum operators are the Toeplitz operator acting on them. In the compact Kähler case strong results about their asymptotic expansion exists. Furthermore, induced concepts are presented, like star products, respectively deformation quantizations, Berezin symbols, Berezin coherent states, and the Berezin transform.

Disciplines :

Mathematics

Author, co-author :

SCHLICHENMAIER, Martin ; University of Luxembourg

External co-authors :

Language :

English

Title :

Berezin-Toeplitz Quantization

Publication date :

2025

Main work title :

Encyclopedia of Mathematical Physics

Publisher :

Elsevier

ISBN/EAN :

978-0-323-95706-9

Pages :

Peer reviewed :

Peer reviewed

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https://api.elsevier.com/content/article/PII:B9780323957038000537?httpAccept=text/xml

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