Spherical Calogero model with oscillator/Coulomb potential: classical case

Abstract

We construct the Hamiltonians and symmetry generators of Calogero-oscillator and Calogero-Coulomb models on the N-dimensional sphere within the matrix-model reduction approach. Our method also produces the integrable Calogero-Coulomb-Stark model on the sphere and proves the integrability of the spin extensions of all these systems.

11 pages, no figures

References in corpus (5)

• Physics and Mathematics of Calogero particles
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• Anisotropic Higgs oscillator

Cited by in corpus (7)

• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• ${\mathbb{C}}^N$-Smorodinsky-Winternitz system in a constant magnetic field
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Hidden symmetries of the Higgs oscillator and the conformal algebra
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanics
• Superintegrable deformations of oscillator and Coulomb systems