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

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