On the Theory of Radiating Electrons

Abstract

In 1938 Dirac[1] showed that the self force on a point electron could be calculated in a consistent manner by assuming that it was due to just part of the field of the electron. Thus by splitting the field into two parts, a radiation field, which gave rise to the self force, and a bound field containing the diverging part of the field, he derived the Lorentz-Dirac equation governing the motion of the electron in an electromagnetic field. We discuss how this theory and the Lorentz-Dirac equation may be derived for each particle of a system of particles using the principle of least action from the action integral,

$${\text{I = }}\int {{{\text{d}}^4}{\text{x}}} \left\{ { - \frac{1}{{8\Pi }}\frac{{^{\partial {\text{A}}}\mu }}{{\partial {{\text{x}}_\nu }}}\frac{{^{\partial {\text{A}}}\mu }}{{\partial {{\text{x}}_\nu }}} + \frac{1}{{\text{c}}}{{\text{j}}_\mu }{{\text{A}}_\mu }} \right\}$$

((1-1))