Overview
- 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
Part of the book series: CRM Short Courses (CRMSC)
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About this book
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.
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Keywords
- Kahler manifolds
- complexified tangent bundle
- complex line bundles
- quantization compact Kahler manifolds
- Berezin-Toeplitz operator
- Schwartz kernels
- Kostant-Souriau operators
- coherent states
- norm correspondence
- Szego projector
- Kaehler manifolds
- graduate text semiclassical analysis
- graduate text quantization
- geometric quantization
- circle bundle
- Berezin–Toeplitz operators course Tel-Aviv
Table of contents (9 chapters)
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Front Matter
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Back Matter
Reviews
“The book … represents an essential prerequisite for anyone who wants to work in the field. The author have managed to make it readable by non-specialists.” (Béchir Dali, zbMATH 1452.32002, 2021)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds
Authors: Yohann Le Floch
Series Title: CRM Short Courses
DOI: https://doi.org/10.1007/978-3-319-94682-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-94681-8Published: 02 October 2018
Softcover ISBN: 978-3-030-06898-1Published: 30 January 2019
eBook ISBN: 978-3-319-94682-5Published: 19 September 2018
Series ISSN: 2522-5200
Series E-ISSN: 2522-5219
Edition Number: 1
Number of Pages: VIII, 140
Number of Illustrations: 160 b/w illustrations, 1 illustrations in colour
Topics: Differential Geometry, Several Complex Variables and Analytic Spaces