English

Quantization of compact symplectic manifolds

Differential Geometry 2017-06-22 v2

Abstract

We develop the theory of Berezin-Toeplitz operator on any compact symplectic prequantizable manifold from scratch. Our main inspiration is the Boutet de Monvel-Guillemin theory, that we simplify in several ways to obtain a concise exposition. A comparison with the spin-c Dirac quantization is also included.

Keywords

Cite

@article{arxiv.1409.8507,
  title  = {Quantization of compact symplectic manifolds},
  author = {Laurent Charles},
  journal= {arXiv preprint arXiv:1409.8507},
  year   = {2017}
}

Comments

Simplified the main proofs on operator composition and added sharp remainder estimates. Version 1 has been published in Journal of Geometric Analysis

R2 v1 2026-06-22T06:09:24.043Z