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

TL;DR

This paper introduces a new multiparticle system model in $$-Poincaré spacetime inspired by 2+1D gravity, emphasizing nonlocal interactions and local deformed conservation laws, differing from existing models.

Contribution

It proposes a novel Lagrangian for multiparticle systems in $$-Poincaré spacetime, incorporating nonlocal interactions and a new approach to particle process locality.

Findings

Derived a new dynamics for interacting particles with $$-momentum space.

Established a model with local deformed energy-momentum conservation laws.

Ensured spacetime transformations preserve the locality of individual particle processes.

Abstract

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. In particular a particle process is characterized by a local deformed energy-momentum conservation law. The spacetime transformations are generated by total charges/generators for the composite particle system, and leave unaffected the locality of individual particle processes.