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Authors:

• Yohann Le Floch⁰

1. Yohann Le Floch

   1. IRMA, Université de Strasbourg, Strasbourg, France
      

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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.

• 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

“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)

• IRMA, Université de Strasbourg, Strasbourg, France

  Yohann Le Floch

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