Relativistic deformed kinematics from locality conditions in a generalized spacetime

TL;DR

This paper introduces a classical framework for deformed relativistic kinematics using a modified composition law of four-momenta, linking it to spacetime structure and comparing it with algebraic and geometric approaches.

Contribution

It provides a novel derivation of isotropic deformed kinematics from locality conditions, connecting classical spacetime modifications with algebraic and geometric models.

Findings

Derived a generic relativistic isotropic deformed kinematics

Linked the deformed composition law to a modified spacetime concept

Compared with $$-Poincare9 Hopf algebra and maximally symmetric momentum space approaches

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.