Relative Locality in $\kappa$-Poincar\'e

TL;DR

This paper interprets the $ppa$-Poincare9 Hopf algebra within curved momentum space, establishing a consistent model of deformed relativistic kinematics that preserves the relativity principle and explores particle interactions.

Contribution

It provides the first coherent model of $ppa$-Poincare9 kinematics with curved momentum space, detailing boost actions and invariance of physical laws.

Findings

Curved momentum space leads to relativity of locality.

Boost transformations depend on particle momenta.

Relativity principle remains valid under deformed boosts.

Abstract

We show that the $\kappa$-Poincar\'e Hopf algebra can be interpreted in the framework of curved momentum space leading to the relativity of locality \cite{AFKS}. We study the geometric properties of the momentum space described by $\kappa$-Poincar\'e, and derive the consequences for particles propagation and energy-momentum conservation laws in interaction vertices, obtaining for the first time a coherent and fully workable model of the deformed relativistic kinematics implied by $\kappa$-Poincar\'e. We describe the action of boost transformations on multi-particles systems, showing that in order to keep covariant the composed momenta it is necessary to introduce a dependence of the rapidity parameter on the particles momenta themselves. Finally, we show that this particular form of the boost transformations keeps the validity of the relativity principle, demonstrating the invariance of the equations of motion under boost transformations.