Radiative Damping and Functional Differential Equations

TL;DR

This paper introduces a novel approach to solving the classical many-body problem with radiative damping by modifying Maxwell's electrodynamics, resulting in functional differential equations that avoid runaway solutions and provide new insights into radiation effects.

Contribution

It presents a new method to handle radiative damping using functional differential equations, improving upon traditional models and enabling more accurate simulations.

Findings

Locally, radiation damping approximates the standard third-order expression.

Globally, solutions exhibit dramatically different properties.

Numerical solutions for the one-body problem demonstrate the approach's effectiveness.

Abstract

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.