Feynman's Electromagnetic Fields Induced by Moving Charges and the Existence and Uniqueness of Solutions to the N-Body Problem of Electrodynamics

Abstract

Given n charges interacting with each other according to Feynman's law. Let (r _j (t), v _j (t)) denote the position and velocity of the charge q _j . The list y(t) of all such vectors is called a trajectory. A Lipschitzian trajectory x(t), (t ≤ 0), with continuous derivative, on which the velocities do not exceed some limiting velocity v < c, where c denotes the speed of light, is called an initial trajectory. A locally Lipschitzian trajectory y(t) is called relativistically admissible if the velocities on it stay below the speed of light c.