Scattering and Radiation Damping in Gyroscopic Lorentz Electrodynamics

The nonlinear system of equations of relativistic Lorentz electrodynamics (LED) is studied in a “gyroscopic setup” in which the Lorentz electron is assumed to remain at rest, leaving the electromagnetic fields and the particle spin as the only dynamical degrees of freedom. The global existence and uniqueness of this gyroscopic spin-plus-field dynamics in unbounded space is proven. It is further shown that for rotation-reflection symmetric initial data any gyroscopic solution also satisfies the world-line equations consistent with a non-moving Lorentz electron, thus furnishing a proper solution of the complete set of equations of LED. Rotation-reflection symmetric scattering is shown to occur for sufficiently small ratio of electrostatic to (positive) bare rest mass, with deviations from the stationary spin state dying out exponentially fast through radiation damping. The previously proven result that the renormalized spinning Lorentz electron evolves like a soliton in scattering processes combined with the present results that scattering does occur establish the solitonic character of the renormalized Lorentz electron. To appear in : Letters in Mathematical Physics c ©2001. The authors. Reproduction for non-commercial purposes, by any means, is permitted.