A brief introduction to Berezin-Toeplitz operators on compact Kahler Manifolds

• 作者： Le Floch, Yohann, author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • CRM short courses.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： CRM short courses,
• 主題： Kahlerian manifolds. , Toeplitz operators. , Differential Geometry. , Several Complex Variables and Analytic Spaces.
• ISBN： 9783319946825 (electronic bk.) 、 9783319946818 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Preface -- 1. Introduction -- 2. A short introduction to Kahler manifolds -- 3. Complex line bundles with connections -- 4. Quantization of compact Kahler 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.
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• 摘要註: This text provides a comprehensive introduction to Berezin-Toeplitz operators on compact Kahler 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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