Quantum surfaces, special functions, and the tunneling effect

DOI10.1023/A:1017905424488zbMath0996.53058arXivmath/0106187MaRDI QIDQ5959039

Mikhail V. Karasev

Publication date: 29 October 2002

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

Full work available at URL: https://arxiv.org/abs/math/0106187

zbMATH Keywords

hypergeometric functionsdeformation quantizationtheta functionsirreducible representationsPoisson manifoldsstar productgeometric quantizationKählerian geometrysymplectic leavestrace formulasWick calculus

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Theta functions and abelian varieties (14K25) Global Riemannian geometry, including pinching (53C20) Deformation quantization, star products (53D55) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

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Symplectic areas, quantization, and dynamics in electromagnetic fields ⋮ Noncommutative algebras, nano-structures, and quantum dynamics generated by resonances. III. ⋮ Magneto-metric Hamiltonians on quantum surfaces in the configuration space ⋮ Secondary resonances in Penning traps. Non-Lie symmetry algebras and quantum states ⋮ Weyl’s symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics ⋮ Eigenstates of the quantum Penning-Ioffe nanotrap at resonance ⋮ Geometric dynamics on quantum nano-surfaces and low-energy spectrum in a homogeneous magnetic field ⋮ Inserted perturbations generating asymptotical integrability

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