Quantization of compact symplectic manifolds

DOI10.1007/s12220-015-9644-0zbMath1357.81127arXiv1409.8507OpenAlexW1773181449MaRDI QIDQ345283

Laurent Charles

Publication date: 1 December 2016

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.8507

zbMATH Keywords

semiclassical limitgeometric quantizationBerezin-Toeplitz operatorsspin-c Dirac operatorsymplectic compact manifold

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Geometry and quantization, symplectic methods (81S10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Geometric quantization (53D50)

Related Items (23)

Berezin-Toeplitz quantization associated with higher Landau levels of the Bochner Laplacian ⋮ Symplectic rigidity and quantum mechanics ⋮ Spectral asymptotics of semiclassical unitary operators ⋮ Equivariant fixed point formulae and Toeplitz operators under Hamiltonian torus actions and remarks on equivariant asymptotic expansions ⋮ An algebra of distributions related to a star product with separation of variables ⋮ Local scaling asymptotics for the Gutzwiller trace formula in Berezin-Toeplitz quantization ⋮ Commutators of spectral projections of spin operators ⋮ Bounds for fidelity of semiclassical Lagrangian states in Kähler quantization ⋮ Berezin-Toeplitz quantization for eigenstates of the Bochner Laplacian on symplectic manifolds ⋮ Sharp correspondence principle and quantum measurements ⋮ Low-energy spectrum of Toeplitz operators with a miniwell ⋮ Asymptotic representations of Hamiltonian diffeomorphisms and quantization ⋮ Fractional exponential decay in the forbidden region for Toeplitz operators ⋮ Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells ⋮ Analytic Bergman operators in the semiclassical limit ⋮ Equivariant asymptotics of Szegö kernels under Hamiltonian \(U(\mathbf{2})\)-actions ⋮ On the composition of Berezin-Toeplitz operators on symplectic manifolds ⋮ Quantum speed limit versus classical displacement energy ⋮ Quantum footprints of Liouville integrable systems ⋮ On polynomials in spectral projections of spin operators ⋮ Inferring topology of quantum phase space ⋮ Berezin-Toeplitz quantization on symplectic manifolds of bounded geometry ⋮ Lagrangian fields, Calabi functions, and local symplectic groupoids

Cites Work

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• Symbolic calculus for Toeplitz operators with half-form
• Toeplitz operators on symplectic manifolds
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• Local cohomology of the algebra of \(C^\infty\) functions on a connected manifold
• Toeplitz quantization of Kähler manifolds and \(gl(N)\), \(N\to \infty\) limits
• Berezin--Toeplitz operators, a semi-classical approach
• Star products on compact pre-quantizable symplectic manifolds
• Stability functions
• Holomorphic Morse inequalities and Bergman kernels
• Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds
• Berezin–Toeplitz quantization on Kähler manifolds
• A note on scaling asymptotics for Bohr-Sommerfeld Lagrangian submanifolds
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Quasimodes and Bohr-Sommerfeld Conditions for the Toeplitz Operators
• On the asymptotic expansion of Bergman kernel

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