Resonance Gyrons and Quantum Geometry

2005/11/07 by Mikhail Karasev, Karasev, Mikhail
Mathematics · Physics and Astronomy · #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math.QA

paper · pdf · doi:10.48550/arxiv.math/0511161

Latex, 31pages

arxiv created 2005/11/07 · openalex publication_date 2005/11/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We 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.

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