Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula

DOI10.1007/s11005-020-01267-zOpenAlexW3105600231MaRDI QIDQ2191213

Louis Ioos

Publication date: 24 June 2020

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.03027

zbMATH Keywords

Hamiltonian flowsgeometric quantizationBerezin-Toeplitz operatorscontact topologyGutzwiller trace formula

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Symplectic and contact topology in high or arbitrary dimension (57R17) Index theory and related fixed-point theorems on manifolds (58J20) Geometry and quantization, symplectic methods (81S10) Geometric quantization (53D50) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (2)

Closed geodesics and pluricanonical sections on ball quotients ⋮ Geometric quantization of symplectic maps and Witten's asymptotic conjecture

Cites Work

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• On the composition of Berezin-Toeplitz operators on symplectic manifolds
• Index and dynamics of quantized contact transformations
• On symplectic cobordisms
• The spin\(^{\mathbf c}\) Dirac operator on high tensor powers of a line bundle
• Superconnection and family Bergman kernels
• Symbolic calculus for Toeplitz operators with half-form
• Semi-classical properties of geometric quantization with metaplectic correction
• Toeplitz operators on symplectic manifolds
• The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
• Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion. II: Direct images and Bott-Chern forms. III: Quillen metrics on holomorphic determinants
• Chaos in classical and quantum mechanics
• Circular symmetry and the trace formula
• Semiclassical spectral estimates for Toeplitz operators
• Semiclassical principal symbols and Gutzwiller's trace formula
• Toeplitz quantization of Kähler manifolds and \(gl(N)\), \(N\to \infty\) limits
• Scalar curvature and projective embeddings. I
• Local scaling asymptotics for the Gutzwiller trace formula in Berezin-Toeplitz quantization
• The semi-classical trace formula and propagation of wave packets
• Berezin-Toeplitz quantization for eigenstates of the Bochner Laplacian on symplectic manifolds
• Holomorphic Morse inequalities and Bergman kernels
• Pointwise Weyl law for partial Bergman kernels
• Quantization of Kähler manifolds. I: Geometric interpretation of Berezin's quantization
• The manifold of compatible almost complex structures and geometric quantization
• The Spectral Theory of Toeplitz Operators. (AM-99)
• QUANTIZATION
• Maximal contact and symplectic structures
• Quantization and unitary representations
• Generalized Bergman kernels on symplectic manifolds
• Holomorphic equivariant analytic torsions

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