Algebra and quantum geometry of multifrequency resonance

DOI10.1070/IM2010v074n06ABEH002520zbMath1211.81080MaRDI QIDQ3074505

E. M. Novikova, Mikhail V. Karasev

Publication date: 9 February 2011

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

zbMATH Keywords

coherent statesalgebra of symmetriesfrequency resonancenon-linear commutation relationsquantum Kähler forms

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Kähler manifolds (32Q15) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Coherent states (81R30) Geometry and quantization, symplectic methods (81S10) Local differential geometry of Hermitian and Kählerian structures (53B35)

Related Items (11)

Coherent Schwartz distributions of the Heisenberg algebra and inverted oscillator ⋮ Minimal basis of the symmetry algebra for three-frequency resonance ⋮ Semiclassical asymptotics of oscillating tunneling for a quadratic Hamiltonian on the algebra \(\operatorname{su}(1,1)\) ⋮ Cubic algebra and averaged Hamiltonian for the resonance \(3: ( - 1)\) Penning-Ioffe trap ⋮ Instantons via breaking geometric symmetry in hyperbolic traps ⋮ Secondary resonances in Penning traps. Non-Lie symmetry algebras and quantum states ⋮ Algebra of symmetries of three-frequency resonance: reduction of a reducible case to an irreducible case ⋮ On calculating the coefficients in the quantum averaging procedure for the Hamiltonian of the resonance harmonic oscillator perturbed by a differential operator with polynomial coefficients ⋮ New approach to the procedure of quantum averaging for the Hamiltonian of a resonance harmonic oscillator with polynomial perturbation for the example of the spectral problem for the cylindrical Penning trap ⋮ Algebra of symmetries of three-frequency hyperbolic resonance ⋮ Inserted perturbations generating asymptotical integrability

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