A brief introduction to Berezin-Toeplitz operators on compact Kähler manifolds

DOI10.1007/978-3-319-94682-5zbMath1452.32002OpenAlexW2892368228MaRDI QIDQ721714

Yohann Le Floch

Publication date: 19 July 2018

Published in: CRM Short Courses (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-94682-5

zbMATH Keywords

connectionsdifferential geometryKähler manifoldsgeometric quantizationcomplex line bundlesBerezin-Toeplitz operators

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Kähler manifolds (32Q15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Geometric quantization (53D50) Holomorphic bundles and generalizations (32L05)

Related Items (15)

The Berezin transform and its applications ⋮ A probabilistic Weyl-law for perturbed Berezin-Toeplitz operators ⋮ Almost representations of algebras and quantization ⋮ Almost sure Weyl law for quantized tori ⋮ WKB eigenmode construction for analytic Toeplitz operators ⋮ Sharp correspondence principle and quantum measurements ⋮ Pairs of spectral projections of spin operators ⋮ Fractional exponential decay in the forbidden region for Toeplitz operators ⋮ Analytic Bergman operators in the semiclassical limit ⋮ Spectral aspects of the Berezin transform ⋮ Categorical perspective on quantization of Poisson algebra ⋮ A generalization of the quantization of Poisson manifolds ⋮ Quantum footprints of Liouville integrable systems ⋮ On polynomials in spectral projections of spin operators ⋮ Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems

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