Tree-level scattering amplitudes in nonlocal field theories

TL;DR

This paper demonstrates that for certain stable and unitary nonlocal field theories, the tree-level scattering amplitudes match those of the corresponding local theories, including nonlocal gravity.

Contribution

It proves equivalence of tree-level scattering amplitudes between specific nonlocal and local field theories using two different methods.

Findings

Tree-level amplitudes in nonlocal theories match local counterparts.

Nonlocal gravity's scattering amplitudes are identical to Einstein's general relativity.

Results hold for theories with stability, unitarity, and super-renormalizability or finiteness.

Abstract

We prove in two ways that, for a special class of nonlocal field theories consistent with linear and non-linear stability at the classical level, and with unitarity and super-renormalizability or finiteness at the quantum level, the $n$-point tree-level scattering amplitudes are the same as those of the underlying local theory. In particular, the $n$-point amplitudes of nonlocal gravity, with or without coupling to matter, are the same as for Einstein's general relativity.