Multi-particle systems in $\kappa$-Poincaré inspired by 2+1D gravity

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/$\kappa$-Poincaré 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.

arXiv commentIn this new version the discussion of our results has been improved. Some parts of the manuscript have been extended. The title and abstract have been slightly modified

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Cited by in corpus (7)

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• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• Spacetime from locality of interactions in deformations of special relativity: the example of $\kappa$-Poincaré Hopf algebra
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• Relative-locality phenomenology on Snyder spacetime
• Effective Chern-Simons actions of particles coupled to 3D gravity
• Physical velocity of particles in relativistic curved momentum space