Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential

Abstract

We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb systems, replacing their angular degrees of freedom by those of a generalized rational Calogero model. Using the action-angle description, it is established that maximal superintegrability is retained. For the rational Calogero model with Coulomb potential, we present all constants of motion via matrix model reduction. In particular, we construct the analog of the Runge-Lenz vector.

arXiv comment7 pages

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Cited by in corpus (21)

• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• Runge-Lenz vector in Calogero-Coulomb problem
• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• ${\mathbb{C}}^N$-Smorodinsky-Winternitz system in a constant magnetic field
• Klein-Gordonization: mapping superintegrable quantum mechanics to resonant spacetimes
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Extended symmetries in geometrical optics
• Dunkl symplectic algebra in generalized Calogero models
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• On symmetries of generalized Calogero model and Polychronakos-Frahm chain
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanics
• Noncompact ${\mathbf{CP}}^N$ as a phase space of superintegrable systems
• Superintegrable deformations of oscillator and Coulomb systems
• Coupling and particle number intertwiners in the Calogero model
• Dynamical symmetries of the Calogero-Coulomb model