Different realizations of kappa-momentum space and relative-locality effect

TL;DR

This paper investigates various realizations of kappa-momentum space within the kappa-Poincare algebra, demonstrating that particle mass remains realization-independent up to linear order, while time delay effects depend on the specific realization chosen.

Contribution

It shows that the particle mass definition in relative locality is realization-independent for many cases, but the time delay formula varies with realization choices.

Findings

Mass definition is realization-independent up to linear order.

Time delay formula depends on the realization of the momentum space.

Different realizations lead to observable differences in time delay predictions.

Abstract

We consider different realizations for the momentum sector of kappa-Poincare Hopf algebra, which is associated with a curved momentum space. We show that the notion of the particle mass as introduced recently by Amelino-Camelia et al. in the context of relative-locality is realization independent for a wide class of realizations, up to linear order in deformation parameter l. On the other hand, the time delay formula clearly shows a dependence on the choice of realization.