Multicomponent Wentzel–Kramers–Brillouin approximation on arbitrary symplectic manifolds: A star product approach

DOI10.1063/1.532450zbMath0935.81021arXivhep-th/9701111OpenAlexW1990036611MaRDI QIDQ4701600

C. Emmrich, Hartmann Römer

Publication date: 21 November 1999

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

Full work available at URL: https://arxiv.org/abs/hep-th/9701111

zbMATH Keywords

quantizationWKB approximationBorn-Oppenheimer approximationstar productWKB ansatzadditional phase

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Deformation quantization, star products (53D55) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items (1)

Algebraic Rieffel induction, formal Morita equivalence, and applications to deformation quantization.

Cites Work

• Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
• New global asymptotics and anomalies for the problem of quantization of the adiabatic invariant
• A pseudo-algebra of observables for the Dirac equation
• Algebras with general commutation relations and their applications. II. Unitary-nonlinear operator equations
• On the propagation of polarization sets for systems of real principal type
• Deformation theory and quantization. I: Deformations of symplectic structures
• On the Born-Oppenheimer approximation of wave operators in molecular scattering theory
• Algebraic index theorem for families
• Geometry of the transport equation in multicomponent WKB approximations
• Fourier integral operators. I
• Quantal phase factors accompanying adiabatic changes

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