Relative locality in κ-Poincaré

Abstract

We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum space leading to relative locality. We study the geometric properties of the momentum space described by κ-Poincaré and derive the consequences for particle 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 κ-Poincaré. We describe the action of boost transformations on multi-particle systems, showing that the covariance of the composed momenta requires a dependence of the rapidity parameter on the particle 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.