Resonance Gyrons and Quantum Geometry

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dc.creatorKarasev, Mikhail
dc.date2005-11-07
dc.date.accessioned2026-07-07T06:50:53Z
dc.date.available2026-07-07T06:50:53Z
dc.descriptionWe describe irreducible representations, coherent states and star-products for algebras of integrals of motions (symmetries) of two-dimensional resonance oscillators. We demonstrate how the quantum geometry (quantum Kähler form, metric, quantum Ricci form, quantum reproducing measure) arises in this problem. We specifically study the distinction between the isotropic resonance $1:1$ and the general $l:m$ resonance for arbitrary coprime $l,m$. Quantum gyron is a dynamical system in the resonance algebra. We derive its Hamiltonian in irreducible representations and calculate the semiclassical asymptotics of the gyron spectrum via the quantum geometrical objects.
dc.descriptionLatex, 31pages
dc.identifierhttps://arxiv.org/abs/math/0511161
dc.identifierhttp://arxiv.org/abs/math/0511161
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104806
dc.subjectQuantum Algebra
dc.titleResonance Gyrons and Quantum Geometry
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