We propose the notion of the oscillator on Kähler space and consider its supersymmetrization in the presence of a constant magnetic field. Supersymmetric mechanics attracts permanent interest since its introduction witten [1]. However, studies focussed mainly on the mechanics with standard N = 2 supersymmetries (see for the review sukh [2] and refs therein). The systems with N = 4 supersymmetri...

We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces I CP, as well as on their non-compact counterparts, i. e. the N−dimensional Lobachewski spaces LN . We find the spectrum of this system and the complete basis of wavefunctions. Surprisingly, the inclusion of a magnetic field does not yield any qualitative change in the energy spectrum. Fo...