MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws

Abstract

In this paper, we analyze the modification of integrable models in the $κ$-deformed space-time. We show that two dimensional isotropic oscillator problem, Kepler problem and MICZ-Kepler problem in $κ$-deformed space-time admit integrals of motion as in the commutative space. We also show that the duality equivalence between $κ$-deformed Kepler problem and $κ$-deformed two-dimensional isotropic oscillator explicitly, by deriving Bohlin-Sundman transformation which maps these two systems. These results are valid to all orders the the deformation parameter.

21 pages, references added, results are valid to all orders in the deformation parameter