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arXiv · hep-th/0309196

3D Oscillator and Coulomb Systems reduced from Kahler spaces

Armen Nersessian·Armen Yeranyan
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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.

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Armen Nersessian, Armen Yeranyan. 2003-09-19. 3D Oscillator and Coulomb Systems reduced from Kahler spaces. https://doi.org/10.1088/0305-4470%2F37%2F7%2F020

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