Multi-center MICZ-Kepler system, supersymmetry and integrability

Abstract

We propose the general scheme of incorporation of the Dirac monopoles into mechanical systems on the three-dimensional conformal flat space. We found that any system (without monopoles) admitting the separation of variables in the elliptic or parabolic coordinates can be extended to the integrable system with the Dirac monopoles located at the foci of the corresponding coordinate systems. Particular cases of this class of system are the two-center MICZ-Kepler system in the Euclidean space, the limiting case when one of the background dyons is located at the infinity as well as the model of particle in parabolic quantum dot in the presence of parallel constant uniform electric and magnetic fields.

5 pages, revtex, revised version

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• Hidden symmetry of hyperbolic monopole motion
• On the nature of fermion-monopole supersymmetry
• Hidden symmetries of two-electron quantum dots in a magnetic field
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• Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory
• Relationship between quantum mechanics with and without monopoles
• N=4, d=1 tensor multiplet and hyper-Kahler sigma-models
• Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
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Cited by in corpus (22)

• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
• Bertrand spacetimes as Kepler/oscillator potentials
• Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds
• Second Hopf map and supersymmetric mechanics with Yang monopole
• Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
• Curved manifolds with conserved Runge-Lenz vectors
• Supergoop Dynamics
• N=4 Supersymmetric MICZ-Kepler systems on S3
• Generalized five-dimensional Kepler system, Yang-Coulomb monopole and Hurwitz transformation
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
• Dynamical supersymmetry of spin particle-magnetic field interaction
• Separability and Dynamical Symmetry of Quantum Dots
• Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration
• Multi-center MICZ-Kepler systems
• Novel symmetries in an interacting N = 2 supersymmetric quantum mechanical model
• Two--center quantum MICZ--Kepler system and the Zeeman effect in the charge-dyon system
• Maxwell fish eye for polarized light
• Generic N=4 supersymmetric hyper-Kähler sigma models in D=1
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra
• On superintegrable monopole systems
• Generalizations of MICZ-Kepler system
• Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution