Algebra of symmetries of three-frequency resonance: reduction of a reducible case to an irreducible case

DOI10.1134/S0001434618110287zbMath1410.81021OpenAlexW2907713311WikidataQ128655778 ScholiaQ128655778MaRDI QIDQ668314

E. M. Novikova, Mikhail V. Karasev

Publication date: 19 March 2019

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434618110287

zbMATH Keywords

coherent statesalgebra of symmetriesfrequency resonancenonlinear commutation relations

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Coherent states (81R30) Applications of functional analysis in quantum physics (46N50) Resonance in context of PDEs (35B34)

Related Items (3)

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

Cites Work

• Advances in quantization: quantum tensors, explicit star-products, and restriction to irreducible leaves
• Minimal basis of the symmetry algebra for three-frequency resonance
• Algebra and quantum geometry of multifrequency resonance
• Multiple wells in the semi-classical limit I
• Birkhoff-Gustavson normal form in classical and quantum mechanics
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