Scattering and radiation damping in gyroscopic Lorentz electrodynamic

Abstract

Relativistic massive Lorentz electrodynamics (LED) is studied in a ``gyroscopic setup'' where the electromagnetic fields and the particle spin are the only dynamical degrees of freedom. A rigorous proof of the global existence and uniqueness of the dynamics is given for essentially the whole range of field strengths reasonable for a classical theory. For a class of rotation-reflection symmetric field data it is shown that the dynamics also satisfies the world-line equations for a non-moving Lorentz electron, thus furnishing rigorous solutions of the full system of nonlinear equations of LED. The previously proven soliton dynamics of the Lorentz electron is further illucidated by showing that rotation-reflection symmetric deviations from the soliton state of the renormalized particle die out exponentially fast through radiation damping if the electrostatic mass is smaller than the bare rest mass.