Retarded field of a uniformly accelerated source in non-local scalar field theory

TL;DR

This paper investigates how non-local scalar field theories affect the retarded field of a uniformly accelerated source, revealing regularization effects and horizon divergences that can be mitigated with specific source configurations.

Contribution

It demonstrates that non-locality regularizes the field at the source but introduces horizon divergences in Lorentz-invariant theories under uniform acceleration.

Findings

Non-locality regularizes the field at the source location.

Divergences occur at the acceleration horizon in these theories.

Proper source placement can remove the horizon divergences.

Abstract

We study the retarded field sourced by a uniformly accelerated particle in a non-local scalar field theory. While the presence of non-locality regularizes the field at the location of the source, we also show that Lorentz-invariant non-local 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 non-local retarded Green function indicate that the divergences can be removed by placing appropriate sources on the acceleration horizon in the asymptotic past.