Pair production in classical electrodynamics

One of the most relevant features of quantum field theory is the phenomenon of pair production, the existence of which, first suggested by Dirac, was not even suspected in the older theories. On the other hand Feynman, in the spirit of his spatiotemporal approach to quantum mechanics, showed how a description of pair production could be given within classical relativistic kinematics; in fact, he actually exhibited world lines with the required properties in the framework of a nonlocal modification of classical electrodynamics conceived by Bopp. In the present paper we show how classical world lines, just of the type required by Feynman to describe the phenomenon of pair production, naturally arise in classical electrodynamics. More precisely, we show that such world lines occur as solutions of the well-known Abraham-Lorentz-Dirac equation, which was originally designed to describe the motion of just a single point charge in self-interaction with the electromagnetic field.