LIVING IN CURVED MOMENTUM SPACE

Abstract

In this paper, we review some aspects of relativistic particles' mechanics in the case of a nontrivial geometry of momentum space. We start by showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled to particles, when (topological) degrees of freedom of gravity are solved for. We argue that there might exist a similar topological phase of quantum gravity in 3+1 dimensions. Then, we characterize the main properties of the theory of interacting particles with curved momentum space and the symmetries of the action. We discuss the space–time picture and the emergence of the principle of relative locality, according to which locality of events is not absolute but becomes observer dependent, in the controllable, relativistic way. We conclude with the detailed review of the most studied κ-Poincaré framework, which corresponds to the de Sitter momentum space.