Isospin particle systems on quaternionic projective spaces

Abstract

We construct the isospin particle system on $n$-dimensional quaternionic projective spaces in the presence of BPST-instanton by the reduction from the free particle on $(2n+1)$-dimensional complex projective space. Then we add to this system a "quaternionic oscillator potential" and show, that this oscillator-like system is superintegrable. We show, that besides the analogs of quadratic constants of motion of the spherical (Higgs) and $\mathbb{C}{P}^n$- oscillators, it possesses the third-order constants of motion, which are functionally independent from the quadratic ones.

8 pages, PACS numbers: 03.65-w, 02.30.Ik, 1 reference added

References in corpus (4)

• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Hyperboloid, instanton, oscillator
• Symmetries of N=4 supersymmetric CP(n) mechanics
• N=2 supersymmetric S^2 -> CP^3 -> S^4 fibration viewed as superparticle mechanics

Cited by in corpus (6)

• ${\mathbb{C}}^N$-Smorodinsky-Winternitz system in a constant magnetic field
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• Hidden symmetries of deformed oscillators
• Superintegrable deformations of oscillator and Coulomb systems
• Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution