  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 covariance. The main result is
that the invariant amplitudes are finite at all orders of the perturbation
theory, due to the finitness of the momentum space. Finally, the relation with
a field theory in spacetime representation is briefly discussed.
