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A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds

  • Yohann Le Floch

Part of the CRM Short Courses book series (CRMSC)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Yohann Le Floch
    Pages 1-6
  3. Yohann Le Floch
    Pages 7-21
  4. Yohann Le Floch
    Pages 23-36
  5. Yohann Le Floch
    Pages 55-62
  6. Yohann Le Floch
    Pages 63-73
  7. Yohann Le Floch
    Pages 75-96
  8. Yohann Le Floch
    Pages 97-113
  9. Yohann Le Floch
    Pages 115-123
  10. Back Matter
    Pages 125-140

About this book

Introduction

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.

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

Authors and affiliations

  • Yohann Le Floch
    • 1
  1. 1.IRMAUniversité de StrasbourgStrasbourgFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-94682-5
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-94681-8
  • Online ISBN 978-3-319-94682-5
  • Series Print ISSN 2522-5200
  • Series Online ISSN 2522-5219
  • Buy this book on publisher's site