A Brief Introduction to Berezin-Toeplitz O...

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Sprache: Englisch

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Beschreibung

This text provides a comprehensive introduction to Berezin¿Toeplitz operators on compact Kähler 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.

Über den Autor

Yohann Le Floch is maître de conférences at Université de Strasbourg, in the Analysis team of the Institut de Recherche Mathématique Avancée. His areas of interest are semiclassical analysis, with a focus on Berezin-Toeplitz operators, and classical and quantum integrable systems.

Zusammenfassung

Presents the first introduction to the subject for non-specialists

Requires only a basic knowledge of differential geometry and analysis

First chapters review the necessary geometric notions to study the field

Includes several exercises and examples serving as tutorials or exam problems

Inhaltsverzeichnis

Preface.- 1. Introduction.- 2. A short introduction to Kähler manifolds.- 3. Complex line bundles with connections.- 4. Quantization of compact Kähler 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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Geometrie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	CRM Short Courses
Inhalt:	viii 140 S. 160 s/w Illustr. 1 farbige Illustr. 140 p. 161 illus. 1 illus. in color.
ISBN-13:	9783319946818
ISBN-10:	3319946811
Sprache:	Englisch
Herstellernummer:	978-3-319-94681-8
Einband:	Gebunden
Autor:	Le Floch, Yohann
Hersteller:	Springer Springer International Publishing AG CRM Short Courses
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 14 mm
Von/Mit:	Yohann Le Floch
Erscheinungsdatum:	02.10.2018
Gewicht:	0,395 kg