A divergence-free approximation of the equations of motion for a relativistic classical charged particle

Abstract

A divergence-free asymptotic approximation is developed for constructing an equation of motion for a radiating classical relativistic charged particle. The formulation employs the point particle limit in a sequence of solutions and the method developed by Dirac in his theory of classical charged particle. Since we use the initial-value approach proposed by Schutz, no runaway solutions exist and the irreversible nature of the particle motion is naturally derived. It is pointed out that the derived Lorentz-Dirac equation should not be regarded as an exact description of the motion of the charged particle holding at all times.