Noncompact ${\mathbf{CP}}^N$ as a phase space of superintegrable systems

Abstract

We propose the description of superintegrable models with dynamical $so(1.2)$ symmetry, and of the generic superintegrable deformations of oscillator and Coulomb systems in terms of higher-dimensional Klein model (the non-compact analog of complex projective space) playing the role of phase space. We present the expressions of the constants of motion of these systems via Killing potentials defining the $su(N.1)$ isometries of the Kähler structure.

11 pages, misprints corrected

References in corpus (5)

• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Lobachevsky geometry of (super)conformal mechanics
• The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization
• Near-horizon dynamics of particle in extreme Reissner-Nordström and Clément-Gal'tsov black hole backgrounds: action-angle variables
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"

Cited by in corpus (1)

• Kähler geometry for $su(1,N|M)$-superconformal mechanics