The alternative to classical mass renormalization for tube-based self-force calculations

To date, classical mass renormalization has been invoked in all tube-based self-force calculations, thus following the method introduced in Dirac’s 1938 calculation of the electromagnetic self-force for the classical radiating electron. In this paper a new tube method is described that does not rely on a mass renormalization procedure. As a result, exact self-force calculations become possible for classical radiating systems of finite size. A new derivation of the Lorentz–Dirac equation is given and the relationship between the new tube method and the classical mass renormalization procedure is explained. It is expected that a similar tube method could be used to obtain rigorous results in the gravitational self-force problem. PACS numbers: 03.50.De, 11.10.Gh, 11.30.-j, 04.25.-g AMS classification scheme numbers: 78A35, 81T16, 83C10