Covariant worldline numerics for charge motion with radiation reaction

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 ð‘†â¢ð¿â¡(2,â„‚) 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.