Living in Curved Momentum Space

Understand

In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space.

• We start with 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.