Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere

Abstract

Using the second Hopf map, we perform the reduction of the eight-dimensional (pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting with a Yang monopole. Then, using a standard trick, we obtain, from the latter system, the pseudospherical and spherical generalizations of the Yang-Coulomb system (the five dimensional analog of MICZ-Kepler system). We present the whole set of its constants of motions, including the hidden symmetry generators given by the analog of Runge-Lenz vector. In the same way, starting from the eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the integrable (pseudo)spherical generalization of the Yang-Coulomb system with the Stark term.

10 pages, PACS: 03.65.-w, 02.30.Ik, 14.80.Hv

References in corpus (9)

• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
• Bertrand spacetimes as Kepler/oscillator potentials
• Second Hopf map and supersymmetric mechanics with Yang monopole
• Relationship between quantum mechanics with and without monopoles
• Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
• Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
• Hyperboloid, instanton, oscillator
• Two--center quantum MICZ--Kepler system and the Zeeman effect in the charge-dyon system
• Dipole transitions and Stark effect in the charge-dyon system

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• The Coulomb problem on a 3-sphere and Heun polynomials
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration
• Hopf maps and Wigner's little groups
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra
• On superintegrable monopole systems
• 16D anisotropic inharmonic oscillator and 9D related (MICZ-)Kepler-like systems
• Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang-Coulomb monopole interaction
• Superintegrable deformations of oscillator and Coulomb systems