A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds
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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.
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.
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
Autor*in
Yohann Le Floch
Themen in »A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds«
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
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“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)
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