Classical electrodynamics of a point particle from action integral

Abstract

A new approach to the classical electrodynamics of a point particle (with arbitrary finite number of electromagnetic moments) is presented. It is argued that the notion of a non-singular pointlike current, previously introduced by the author, appropriately describes an electromagnetic point particle. This current is then used in the most standard action integral of an electromagnetic field in interaction with matter to yield a non-singular theory. In the simplest cases this theory yields the Lorentz–Dirac equation of motion of a point charge, or its generalization together with the spin equation of motion for a point charge with an intrinsic magnetic dipole moment. No approximations are involved. From the general theory the conservation of the energy-momentum and of the angular momentum follows.