Covariant dynamics on the energy-momentum space: Scalar field theory

A scalar field theory is constructed on an energy-momentum background of constant curvature. The generalization of the usual Feynamn rules for the flat geometry follows from the requirement of their co-variance. The main result is that the invariant amplitudes are finite at all orders of the perturbation theory, due to the finiteness of the momentum space. Finally, the relation with a field theory in spacetime represen-tation is briefly discussed.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org/licenses/by /4 .0/). Funded by SCOAP3.