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

TL;DR

This paper develops a covariant scalar field theory on a curved energy-momentum space, demonstrating all-order finiteness of amplitudes and connecting it to traditional spacetime field theories.

Contribution

It introduces a covariant scalar field theory on a curved energy-momentum background with finite amplitudes at all perturbation orders.

Findings

Invariant amplitudes are finite at all orders.

The theory generalizes Feynman rules for curved energy-momentum space.

Connection to spacetime field theory is discussed.

Abstract

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.