Unitarity of Minkowski non-local theories made explicit

TL;DR

This paper demonstrates how to explicitly establish the perturbative unitarity of Minkowski non-local scalar field theories by using a modified amplitude calculation prescription involving analytic continuation from Euclidean space.

Contribution

It introduces a novel prescription for computing scattering amplitudes in non-local theories, ensuring unitarity in Minkowski space through analytic continuation from Euclidean results.

Findings

Perturbative unitarity can be achieved in Minkowski non-local theories.

A modified prescription for amplitude calculation is proposed.

Analysis of a non-local φ^4 model illustrates the approach.

Abstract

In this work we explicitly show that the perturbative unitarity of analytic infinite derivative (AID) scalar field theories can be achieved using a modified prescription for computing scattering amplitudes. The crux of the new prescription is the analytic continuation of a result obtained in the Euclidean signature to the Minkowski external momenta. We intensively elaborate an example of a non-local $\phi^4$ model for various infinite derivative operators. General UV properties of amplitudes in non-local theories are discussed.