Multi-particle systems in $\kappa$-Poincar\'e inspired by 2+1D gravity

Understand

Inspired by a Chern-Simons description of 2+1D gravity coupled to point particles we propose a new Lagrangian of a multiparticle system living in $\kappa$-Minkowski/$\kappa$-Poincar\'e spacetime.

• We derive the dynamics of interacting particles with $\kappa$-momentum space, alternative to the one proposed in the "principle of relative locality" literature.
• The model that we obtain takes into account of the nonlocal topological interactions between the particles, so that the effective multi-particle action is not a sum of their free actions.
• In this construction the locality of particle processes is naturally implemented, even for distant observers.