On the self energy and the radiation reaction problem in classical electrodynamics

Abstract

In his fundamental paper "Classical theory of radiating electrons" P.A.M Dirac developed a relativistic covariant equation of motion for a charged point-like particle in flat space-time, the (Abraham-)Lorentz-Dirac equation. From a physical point of view this equation of motion has several unsatisfactory features like the runaway behavior or the so called preacceleration. Theorems on the occurrence of runaway modes e.g. Coleman`s theorem and the Herglotz-Wildermuth theorem, will be investigated. The correctness and physical validity of the Lorentz-Dirac equation has been questioned since its first appearance due to some subtle points in its derivation. For this reason the most authoritative derivation by Dirac and also Baruts were investigated and will be presented in full detail in this thesis and it is also shown that the Herglotz-Wildermuth theorem is not completely true generally. The Model of Topological Fermions (MTF) provides an alternative formulation of charged particles and their interaction in an unified way. In this thesis a proof for the non existence of runaway modes in the MTF is given. Runaway modes appear in many theories and therefore several authors have developed some ideas and methods for the elimination of these unphysical features. Until now no global elimination concept exists. In this thesis a speculation for such an elimination concept will be presented. Furthermore an explicit mathematical proof is given that in the MTF model no 4/3 problem appears.