doi:10.1103/PhysRevD.104.024017engRelancio J.J.Geometry of multiparticle systems with a relativistic deformed kinematics and the relative locality principleART-2021-126242There 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 multiparticle 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 multiparticle system in which locality of interactions is recovered. © 2021 American Physical Society.2021http://zaguan.unizar.es/record/11967910.1103/PhysRevD.104.024017http://zaguan.unizar.es/record/119679oai:zaguan.unizar.es:119679Physical Review D 104, 2 (2021), 024017 [13 pp]All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess