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

Abstract

We study presence of an additional symmetry of a generic central potential in the κ-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 κ-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 κ-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 → 0. 02.30.Ik, 45.20.D, 02.40.Gh. PACS:

Hawking radiation in κ-spacetime

“…Also, one may get a dependence through a deformed m appearing in eqn. (68) (see [37][38][39]53] (25) and (27)). Note that the dependence ofr and r s on a is through the combination ak 0 .…”

“…This mapping is used to obtain a commutative models equivalent to the given κ-deformed model [35,36]. This approach was used to analyze Kepler system in κ-deformed spacetime and it was found that the deformed problem retains all the symmetries as the commutative Kepler problem [37][38][39]. Using this approach, change in the dimension of κ-spacetime with probe scale was analyzed in [40][41][42].…”

Regularization of central forces with damping in two and three dimensions

“…In [27][28][29], we have studied the regularization of central potentials in non-commutative space-time. Thus it is of interest to see whether the results obtained here can be generalized to non-commutative space-time.…”

Regularization of Kepler problem in κ-spacetime

“…Expressing the potential in terms of ordinary spacetime variables, using eqns. ( 3) and ( 4), we obtain (see [27,28] for details).…”

“…A generalization of Kepler problem to the κ-deformed case is constructed [27], which reduces to the commutative problem as we set the deformation parameter to zero. More about studies on κ-deformed Kepler problem can be seen in [26,27,28]. The main calculation is performed via the determination of the explicit transformation formulas for stereographic projection on the κ-plane.…”