Relativistic deformed kinematics from locality conditions in a generalized spacetime

Abstract: We show how a deformed composition law of four-momenta can be used to define, at the classical level, a modified notion of spacetime for a system of two particles through the crossing of worldlines in particle interactions. We present a derivation of a generic relativistic isotropic deformed kinematics and discuss the complementarity and relations with other derivations based on $\kappa$-Poincar\'e Hopf algebra or on the geometry of a maximally symmetric momentum space.