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A brief introduction to Berezin-Toep...

Le Floch, Yohann.

A brief introduction to Berezin-Toeplitz operators on compact Kahler Manifolds

Record Type:	Electronic resources : Monograph/item
Title/Author:	A brief introduction to Berezin-Toeplitz operators on compact Kahler Manifoldsby Yohann Le Floch.
Author:	Le Floch, Yohann.
Published:	Cham :Springer International Publishing :2018.
Description:	viii, 140 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Kahlerian manifolds.
Online resource:	https://doi.org/10.1007/978-3-319-94682-5
ISBN:	9783319946825$q(electronic bk.)

A brief introduction to Berezin-Toeplitz operators on compact Kahler Manifolds
Le Floch, Yohann.

A brief introduction to Berezin-Toeplitz operators on compact Kahler Manifolds[electronic resource] /by Yohann Le Floch. - Cham :Springer International Publishing :2018. - viii, 140 p. :ill., digital ;24 cm. - CRM short courses,2522-5200. - CRM short courses..

Preface -- 1. Introduction -- 2. A short introduction to Kahler manifolds -- 3. Complex line bundles with connections -- 4. Quantization of compact Kahler manifolds -- 5. Berezin-Toeplitz operators -- 6. Schwartz kernels -- 7. Asymptotics of the projector Pi_k -- 8. Proof of product and commutator estimates -- 9. Coherent states and norm correspondence -- A. The circle bundle point of view -- Bibliography.

This text provides a comprehensive introduction to Berezin-Toeplitz operators on compact Kahler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises.

ISBN: 9783319946825$q(electronic bk.)

Standard No.: 10.1007/978-3-319-94682-5doiSubjects--Topical Terms:

793001
Kahlerian manifolds.

LC Class. No.: QA649 / .L445 2018

Dewey Class. No.: 516.36

A brief introduction to Berezin-Toeplitz operators on compact Kahler Manifolds
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505 0 $a Preface -- 1. Introduction -- 2. A short introduction to Kahler manifolds -- 3. Complex line bundles with connections -- 4. Quantization of compact Kahler manifolds -- 5. Berezin-Toeplitz operators -- 6. Schwartz kernels -- 7. Asymptotics of the projector Pi_k -- 8. Proof of product and commutator estimates -- 9. Coherent states and norm correspondence -- A. The circle bundle point of view -- Bibliography.
520 $a This text provides a comprehensive introduction to Berezin-Toeplitz operators on compact Kahler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises.
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