On the electrodynamic group: The relativistic radiation reaction force

Abstract

The relativistic force exerted by a classical electromagnetic field on an electron is examined from the point of view that associates the differential geometry of the space-time trajectory with a continuous group of transformations. The group relevant to this particular case is the group generated by the electromagnetic field tensor (electrodynamic group), This group is studied in some detail by treating separately the two parts of the Lienard-Wiechert expression for the tenser. The intrinsic differential equations of the space-time trajectories associated with the electrodynamic group are obtained by the Cartan method of the moving frame. These equations show that the curvature of the trajectory is associated only with the generalized Coulomb held and the hypertorsion with the radiation field. According to these equations, the relativistic force may have two components along orthogonal spacelike directions: The first, an apparent force, reduces to the Coulomb force in the nonrelativistic limit. The other is orthogonal to the four-momentum and to the apparent force

this is the radiation reaction force. In the nonrelativistic limit it manifests itself as a frictional force reducing the momentum. The approach also offers a point of view of the conventional treatment of radiation reaction in which the nonlocality in time emerges from the geometry of the problem. The implications pertaining to Other areas of physics of the causal connection found between the hypertorsion and the radiation field are briefly considered. (C) 1998 American Institute of Physics.