Curved Momentum Space, Locality, and Generalized Space-Time

Abstract

We establish the correspondence between two apparently unrelated but in fact complementary approaches of a relativistic deformed kinematics: the geometric properties of momentum space and the loss of absolute locality in canonical space-time, which can be restored with the introduction of a generalized space-time. This correspondence is made explicit for the case of κ-Poincaré kinematics and compared with its properties in the Hopf algebra framework.