Brief Introduction to Berezin-Toeplitz Operators on Compact Kahler Manifolds

Brief Introduction to Berezin-Toeplitz Operators on Compact Kahler Manifolds

Le Floch, Yohann

Springer International Publishing AG

10/2018

140

Dura

Inglês

9783319946818

15 a 20 dias

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.
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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