Two derivations of the Feynman formulae for the fields of a moving charge

Abstract

The Feynman expressions for the electric and magnetic fields of a charge moving on an arbitrary trajectory are found by two simple methods. The first involves a direct integration of Maxwell's time-dependent equations. The second is based on the formalism of quantum optics which uses the first order equations of motion for creation and annihilation operators. As an illustration of the simplicity of these methods, the fields of an oscillating electric dipole are obtained.