  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 Lorentz 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.
