(Super)Oscillator on CP(N) and Constant Magnetic Field

Details (Super)Oscillator on CP(N) and Constant Magnetic Field (Super)Oscillator on CP(N) and Constant Magnetic Field

2002-11-08

arxiv.org/abs/hep-th/0211070v6

Phys.Rev. D67 (2003) 065013; Erratum-ibid. D71 (2005) 089901

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, one important statement corrected, PACS numbers: 03.65-w, 11.30.Pb

Scientific paper

10.1103/PhysRevD.67.065013

We define the "maximally integrable" isotropic oscillator on CP(N) and discuss its various properties, in particular, the behaviour of the system with respect to a constant magnetic field. We show that the properties of the oscillator on CP(N) qualitatively differ in the N>1 and N=1 cases. In the former case we construct the ``axially symmetric'' system which is locally equivalent to the oscillator. We perform the Kustaanheimo-Stiefel transformation of the oscillator on CP(2) and construct some generalized MIC-Kepler problem. We also define a N=2 superextension of the oscillator on CP(N) and show that for N>1 the inclusion of a constant magnetic field preserves the supersymmetry of the system.

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