SCALING ASYMPTOTICS FOR QUANTIZED HAMILTONIAN FLOWS

DOI10.1142/S0129167X12501029zbMath1255.53066arXiv1105.4729OpenAlexW2086760853MaRDI QIDQ4902690

Roberto Paoletti

Publication date: 17 January 2013

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.4729

zbMATH Keywords

Toeplitz operatorsHamiltonian flowsBerezin-Toeplitz quantizationSzegö kernelpositive line bundle

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Geometry and quantization, symplectic methods (81S10) Geometric quantization (53D50) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (4)

Local scaling asymptotics for the Gutzwiller trace formula in Berezin-Toeplitz quantization ⋮ Central limit theorem for spectral partial Bergman kernels ⋮ Scaling asymptotics for Szegő kernels on Grauert tubes ⋮ Local scaling asymptotics in phase space and time in Berezin–Toeplitz quantization

Cites Work

• General concept of quantization
• Index and dynamics of quantized contact transformations
• Connections of Berry and Hannay type for moving Lagrangian submanifolds
• On a set of polarized Kähler metrics on algebraic manifolds
• Szegö kernels, Toeplitz operators, and equivariant fixed point formulae
• Universality and scaling of correlations between zeros on complex manifolds
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• Star products on compact pre-quantizable symplectic manifolds
• Holomorphic Morse inequalities and Bergman kernels
• Local trace formulae and scaling asymptotics for general quantized Hamiltonian flows
• Coherent states and projective representation of the linear canonical transformations
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Generalized Bergman kernels on symplectic manifolds

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