Generally covariant formulation of Relative Locality in curved spacetime

Understand

We construct a theory of particles moving in curved both momentum space and spacetime, being a generalization of Relative Locality.

• We find that in order to construct such theory, with desired symmetries, including the general coordinate invariance, we have to use non local position variables.
• It turns out that free particles move on geodesics and momentum dependent translations of Relative Locality are replaced with momentum dependent geodesic deviations.