Causality Violation in Non-local Quantum Field Theory

TL;DR

This paper investigates causality violations in non-local quantum field theory, revealing energy-dependent growth patterns and proposing scenarios to mitigate high-energy causality issues.

Contribution

It provides a detailed analysis of causality violation growth in non-local phi^4 theory, including suppression effects at moderate energies and potential evasion strategies at high energies.

Findings

Causality violation grows with energy in certain processes.

Suppressed causality violation at low to moderate energies.

Rapid exponential growth of causality violation at high energies.

Abstract

We study the causality violation in the non-local phi ^{4}-theory (as formulated by Kleppe and Woodard) containing a finite mass scale Lambda . Starting from the Bogoliubov-Shirkov criterion for causality, we construct and study combinations of S-matrix elements that signal the violation of causality in the one loop approximation. We find that the causality violation in the exclusive process \phi +\phi --> \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--> \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 suggest a scenario, based on an earlier work, that will enable one to evade a large theoretical causality violation at high energies, should it be unobserved experimentally.