Causality Violation in Non-local QFT

TL;DR

This paper investigates causality violations in non-local quantum field theories, showing that violations grow with energy and are suppressed at low energies but become significant near the non-locality scale, with some processes exhibiting exponential growth.

Contribution

It provides a detailed analysis of causality violation growth in non-local QFT, including one-loop and all-order considerations, and offers interpretations of these effects.

Findings

Causality violation grows with energy in non-local QFT.

Suppression of causality violation at low to moderate energies.

Rapid exponential growth of causality violation near the non-locality scale.

Abstract

We study the causality violation in the non-local quantum field theory (as formulated by Kleppe and Woodard) containing a finite mass scale $\Lambda $. We use $\phi ^{4}$ theory as a simple model for study. Starting from the Bogoliubov-Shirkov criterion for causality, we construct and study combinations of S-matrix elements that signal violation of causality in the one loop approximation. We find that the causality violation in the exclusive process $\phi +\phi \to \phi +\phi $ grows with energy, but the growth with energy, (for low to moderate energies) is suppressed to all orders compared to what one would expect purely from dimensional considerations. We however find that the causality violation in other processes such as $\phi +\phi \to \phi +\phi +\phi +\phi $ grows with energy as expected from dimensional considerations at low to moderate energies. For high enough energies comparable to the mass scale $\Lambda $, however, we find a rapid (exponential-like) growth in the degree of causality violation. We generalize some of the 1-loop results to all orders. We present interpretations of the results based on possible interpretations of the non-local quantum field theory models.