Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time

Abstract

We study the presence of an additional symmetry of a generic central potential in the κ space-time. An explicit construction of Fradkin, Bacry, Ruegg and Souriau (FBRS) for a central potential is carried out and the piecewise conserved nature of the vector is established. We also extend the study to Kepler systems with a drag term, particularly the Gorringe-Leach equation is generalized to the κ-deformed space. The possibility of mapping a Gorringe-Leach equation to an equation without drag term is exploited associating a similar conserved vector to the system with a drag term. An extension of the duality between two classes of central potential is introduced in the κ-deformed space and is used to investigate the duality existing between two classes of Gorringe-Leach equations. All the results obtained can be retraced to the correct commutative limit as we let a → 0.