Retarded field of a uniformly accelerated source in nonlocal scalar field theory

We study the retarded field sourced by a uniformly accelerated particle in a nonlocal scalar field theory. While the presence of nonlocality regularizes the field at the location of the source, we also show that Lorentz-invariant nonlocal field theories are particularly sensitive to the somewhat unphysical assumption of uniform acceleration, leading to logarithmic divergences on the acceleration horizon. Analytic properties of the nonlocal retarded Green function indicate that the divergences can be removed by placing appropriate sources on the acceleration horizon in the asymptotic past.