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

TL;DR

This paper investigates the symmetry properties of central potentials in $kappa$-space-time, constructing conserved vectors and extending duality concepts to deformed space, including systems with drag terms.

Contribution

It explicitly constructs the FBRS vector in $kappa$-space-time and extends the duality between classes of Gorringe-Leach equations to this deformed setting.

Findings

Established the piece-wise conserved nature of the FBRS vector.

Generalized Gorringe-Leach equations to $kappa$-deformed space.

Linked duality between classes of central potentials in deformed space.

Abstract

We study presence of an additional symmetry of a generic central potential in the $\kappa$-space-time. An explicit construction of Fradkin and Bacry, Ruegg, Souriau (FBRS) for a central potential is carried out and the piece-wise conserved nature of the vector is established. We also extend the study to Kepler systems with a drag term, particularly Gorringe-Leach equation is generalized to the $\kappa$-deformed space. The possibility of mapping Gorringe-Leach equation to an equation with out drag term is exploited in associating a similar conserved vector to system with a drag term. An extension of duality between two class of central potential is introduced in the $\kappa$-deformed space and is used to investigate the duality existing between two class of Gorringe-Leach equations. All the results obtained can be retraced to the correct commutative limit as we let $a \rightarrow 0$.