Radiative Damping and Functional Differential Equations

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations. Using recently developed numerical techniques for stiff FDEs, we solve these equations for the one-body central force problem with radiative damping with a view to benchmark our new approach. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two body problem and applications to quantum field theory and quantum mechanics.