Spacetime from locality of interactions in deformations of special relativity: the example of $\kappa$-Poincar\'e Hopf algebra

TL;DR

This paper proposes a new way to define spacetime in relativistic physics by modifying how momenta combine, using the $$-Poincare9 Hopf algebra as a specific example, emphasizing locality of interactions.

Contribution

It introduces a novel framework linking spacetime structure to the locality of interactions through modified momentum composition laws, exemplified by the $$-Poincare9 Hopf algebra.

Findings

Spacetime can be derived from interaction locality principles.

The $$-Poincare9 Hopf algebra fits within this new framework.

Modified momentum composition laws influence the structure of spacetime.

Abstract

A new proposal for the notion of spacetime in a relativistic generalization of special relativity based on a modification of the composition law of momenta is presented. Locality of interactions is the principle which defines the spacetime structure for a system of particles. The formulation based on $\kappa$-Poincar\'e Hopf algebra is shown to be contained in this framework as a particular example.