MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws

TL;DR

This paper explores the modifications of classical integrable models like the Kepler and MICZ-Kepler problems in $$-deformed space-time, demonstrating their integrals of motion and a duality via Bohlin-Sundman transformation, valid to all orders of deformation.

Contribution

It establishes the existence of integrals of motion for these models in $$-deformed space and explicitly derives the duality transformation between the Kepler and oscillator problems.

Findings

Integrals of motion are preserved in $$-deformed space for these models.

The Bohlin-Sundman transformation maps $$-deformed Kepler problem to the oscillator.

Duality between Kepler and oscillator models holds to all orders of deformation.

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.