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We consider different realizations for the momentum sector of kappa-PoincareHopf algebra, which is associated with a curved momentum space. We show thatthe notion of the particle mass as introduced recently by Amelino-Camelia etal. in the context of relative-locality is realization independent for a wideclass of realizations, up to linear order in deformation parameter l. On theother hand, the time delay formula clearly shows a dependence on the choice ofrealization.

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