3D Oscillator and Coulomb Systems reduced from Kahler spaces

Abstract

We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kahler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid are originated. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is non-Kahler one. Finally, we extend these results to the family of Kahler spaces with conic singularities.

arXiv commentTo the memory of Professor Valery Ter-Antonyan, 11 pages

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Cited by in corpus (6)

• A maximally superintegrable system on an n-dimensional space of nonconstant curvature
• Quantum Mechanics Model on Kähler conifold
• Quantum Oscillator on $\DC P^n$ in a constant magnetic field
• Elements of (super-)Hamiltonian Formalism
• Hopf maps and Wigner's little groups
• Quantum oscillator on complex projective space (Lobachewski space) in constant magnetic field and the issue of generic boundary conditions