Non-unitarity of Minkowskian non-local quantum field theories

TL;DR

This paper demonstrates that Minkowskian non-local quantum field theories violate unitarity, unlike their Euclidean counterparts, due to differences in how their amplitudes satisfy Cutkosky rules.

Contribution

It provides a clear analysis showing the failure of unitarity in Minkowskian non-local QFTs through one-loop diagram calculations.

Findings

Minkowskian non-local QFTs are not unitary.

The imaginary part of amplitudes does not follow Cutkosky rules.

Euclidean non-local QFTs satisfy Cutkosky rules.

Abstract

We show that Minkowskian non-local quantum field theories are not unitary. We consider a simple one loop diagram for a scalar non-local field and show that the imaginary part of the corresponding complex amplitude is not given by Cutkosky rules, indeed this diagram violates the unitarity condition. We compare this result with the case of an Euclidean non-local scalar field, that has been shown to satisfy the Cutkosky rules, and we clearly identify the reason of the breaking of unitarity of the Minkowskian theory.