CAUSALITY VIOLATION IN NONLOCAL QUANTUM FIELD THEORY

We study the causality violation in the nonlocal ϕ4-theory (as formulated by Kleppe and Woodard) containing a finite mass scale Λ. 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 ϕ+ϕ→ϕ+ϕ 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 ϕ+ϕ→ϕ+ϕ+ϕ+ϕ grows with energy as expected from dimensional considerations at low to moderate energies. For high enough energies comparable to the mass scale Λ, 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.