MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws

Abstract

In this paper, we analyze the modification of integrable models in the $\kappa$-deformed space-time. We show that two dimensional isotropic oscillator problem, Kepler problem and MICZ-Kepler problem in $\kappa$-deformed space-time admit integrals of motion as in the commutative space. We also show that the duality equivalence between $\kappa$-deformed Kepler problem and $\kappa$-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

References in corpus (6)

• New realizations of Lie algebra kappa-deformed Euclidean space
• Covariant realizations of kappa-deformed space
• Bertrand spacetimes as Kepler/oscillator potentials
• Newton's Equation on the kappa space-time and the Kepler problem
• Closedness of orbits in a space with SU(2) Poisson structure
• Central force problem in space with SU(2) Poisson structure

Cited by in corpus (5)

• Jacobi-Maupertius metric and Kepler equation
• Hawking radiation in the kappa-spacetime
• Newtonian cosmology and Evolution of kappa-deformed universe
• Non-Commutative space-time and Hausdorff dimension
• Regularization of Kepler Problem in $\kappa$-spacetime