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arXiv · 2105.12573

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

J. J. Relancio
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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.

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J. J. Relancio. 2021-05-24. Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle. https://doi.org/10.1103/physrevd.104.024017

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