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.

7 pages

References in corpus (2)

• Physics and Mathematics of Calogero particles
• Action-angle variables for dihedral systems on the circle

Cited by in corpus (8)

• Klein-Gordonization: mapping superintegrable quantum mechanics to resonant spacetimes
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Dunkl symplectic algebra in generalized Calogero models
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Coupling and particle number intertwiners in the Calogero model
• Dynamical symmetries of the Calogero-Coulomb model
• Superintegrable deformations of oscillator and Coulomb systems