We discuss radiation reaction effects on charges propagating in ultra-intense laser fields. Our analysis is based on an analytic solution of the Landau-Lifshitz equation. We suggest to measure radiation reaction in terms of a symmetry breaking parame
ter associated with the violation of null translation invariance in the direction opposite to the laser beam. As the Landau-Lifshitz equation is nonlinear the energy transfer within the pulse is rather sensitive to initial conditions. This is elucidated by comparing colliding and fixed target modes in electron laser collisions.
We develop a numerical formulation to calculate the classical motion of charges in strong electromagnetic fields, such as those occurring in high-intensity laser beams. By reformulating the dynamics in terms of SL(2,C) matrices representing the Loren
tz group, our formulation maintains explicit covariance, in particular the mass-shell condition. Considering an electromagnetic plane wave field where the analytic solution is known as a test case, we demonstrate the effectiveness of the method for solving both the Lorentz force and the Landau-Lifshitz equations. The latter, a second order reduction of the Lorentz-Abraham-Dirac equation, describes radiation reaction without the usual pathologies.
