A Brief Introduction to Berezin-Toeplitz Operators on Compact Kähler Manifolds
题名:
A Brief Introduction to Berezin-Toeplitz Operators on Compact Kähler Manifolds
ISBN:
9783319946825
版:
1st ed. 2018.
PRODUCTION_INFO:
Cham : Springer International Publishing : Imprint: Springer, 2018.
物理描述:
VIII, 140 p. 161 illus., 1 illus. in color. online resource.
系列:
CRM Short Courses,
内容:
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.
摘要:
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.
附加团体著者:
语言:
英文