紧凑凯勒流形上的贝里兹-托伊贝尔德算子简介
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.
这篇文章为紧致凯勒流形上的伯埃林-托佩利茨算子提供了全面介绍。本书的核心部分致力于证明这些算子的主要性质，这些性质在诸如复几何、拓扑量子场论、可积系统以及关于辛拓扑与量子力学之间联系的研究中扮演了重要角色。本书精心设计以确保研究生能够获得一种独特的进入该主题的方式。第一部分包含了相关复杂几何材料的回顾，细节和计算明确展示；已尽可能减少先修要求。读者被鼓励通过完成许多简易练习来加深对内容的理解。
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