Connections on Lagrangian submanifolds and some quasiclassical approximation problems

DOI10.1007/BF01480686zbMath0780.58051MaRDI QIDQ684934

Mikhail V. Karasev

Publication date: 15 September 1993

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

zbMATH Keywords

Lagrangian submanifoldsquantization conditionHeisenberg algebra representationzero- curvature connection

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) Geometry and quantization, symplectic methods (81S10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (8)

On the geometry of slow-fast phase spaces and the semiclassical quantization ⋮ Maslov's canonical operator in arbitrary coordinates on the Lagrangian manifold ⋮ Optimal error estimate of the extended-WKB approximation to the high frequency wave-type equation in the semi-classical regime ⋮ Semiclassical asymptotics of oscillating tunneling for a quadratic Hamiltonian on the algebra \(\operatorname{su}(1,1)\) ⋮ Coherent transform of the spectral problem and algebras with nonlinear commutation relations. ⋮ Eigenstates of the quantum Penning-Ioffe nanotrap at resonance ⋮ Global geometrical optics method for vector-valued Schrödinger problems ⋮ Representation of exact and semiclassical eigenfunctions via coherent states. The hydrogen atom in a magnetic field

Cites Work

• Flat Poisson manifolds and finite-dimensional pseudogroups
• Quantal phase factors accompanying adiabatic changes
• Quantization and unitary representations
• On geometric quantization and its connections with the Maslov theory
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