Self-dressing and radiation reaction in classical electrodynamics

Abstract

A canonical approach to self-dressing in classical electrodynamics is presented. A slowly moving, rigid charge distribution is assumed to be completely deprived of the transverse electric E⊥ at an initial time t1' and the development of this component of the field is studied for t > t1' by solving the coupled charge-field Hamilton equations of motion. The theory is specialized to charge distributions of spherical symmetry, and in particular the point-charge, the spherical shell of charge and the spherical volume of charge are considered. As for the dynamics of the charge, the radiation-reaction force during self-dressing is obtained and it is shown to be substantially different at short times from the familiar form obtained for fully dressed charges, although it reduces to the latter for times longer than the time taken by the light to traverse the charge. Finally the most prominent features of the solution of the charge equation of motion for short times are discussed. As for the field, an auxiliary field Ec is introduced which is related to E⊥ and which has the advantage of being easily calculable. It is shown that Ec propagates causally for all the charge distributions considered and the way in which E⊥ can be obtained from Ec is illustrated. In addition it is shown that the radiation-reaction force is very simply related to the force exerted on the charge by Ec alone. In this way the details of the time dependence of the radiation-reaction force can be understood in terms of the behaviour of the field during self-dressing. It is argued that the results obtained for the classical model are capable of shedding light on fundamental issues of quantum electrodynamics, such as the theory of measurement of the field amplitude and the onset of irreversible behaviour during self-dressing.