3D Oscillator and Coulomb Systems reduced from Kahler spaces

Details 3D Oscillator and Coulomb Systems reduced from Kahler spaces 3D Oscillator and Coulomb Systems reduced from Kahler spaces

2003-09-19

arxiv.org/abs/hep-th/0309196v1

J.Phys.A37:2791-2802,2004

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0305-4470/37/7/020

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.

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