English

3D Oscillator and Coulomb Systems reduced from Kahler spaces

High Energy Physics - Theory 2008-11-26 v1 Mathematical Physics math.MP Exactly Solvable and Integrable Systems Quantum Physics

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.

Keywords

Cite

@article{arxiv.hep-th/0309196,
  title  = {3D Oscillator and Coulomb Systems reduced from Kahler spaces},
  author = {Armen Nersessian and Armen Yeranyan},
  journal= {arXiv preprint arXiv:hep-th/0309196},
  year   = {2008}
}

Comments

To the memory of Professor Valery Ter-Antonyan, 11 pages