Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle

Abstract

There is a vast literature showing the connection between a deformed relativistic kinematics and a curved momentum space, and, in particular, how the former can be obtained from the geometrical properties of the latter. However, there is not any mention about the geometry of a multi-particle system making manifest a possible modification in the metric of one particle due to the presence of others. In this work we explore how a curved momentum metric depending on the particles involved in an interaction arises when considering a process. We also show that the principle of relative locality obtained in doubly special relativity from an action is achieved in this geometrical framework in a direct fashion. Moreover, this formalism allows us to generalize this principle when a curvature of spacetime is present in a natural way. Furthermore this geometrical setup allows us to define a new momentum dependent space-time coordinates for a multi-particle system in which locality of interactions is recovered.

arXiv comment14 pages

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• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Reinterpreting deformed Heisenberg algebras
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Relativistic deformed kinematics: from flat to curved spacetimes
• Cosmic Neutrinos as a Window to Departures from Special Relativity
• Non-local quantum field theory from doubly special relativity
• Towards quantum Mechanics on the curved cotangent bundle
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity