Tree-level scattering amplitudes in nonlocal field theories

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.