Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds

AvYohann Le Floch

Inbunden, Engelska, 2018

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2018-10-02
Mått:155 x 235 x 11 mm
Vikt:376 g
Format:Inbunden
Språk:Engelska
Serie:CRM Short Courses
Antal sidor:140
Förlag:Springer International Publishing AG
ISBN:9783319946818

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Mer om författaren

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.

Recensioner i media

“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)

Innehållsförteckning

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.