Covariant Worldline Numerics for Charge Motion with Radiation Reaction

TL;DR

This paper introduces a covariant numerical method using SL(2,C) matrices to accurately simulate charge motion with radiation reaction in strong electromagnetic fields, ensuring physical constraints are preserved.

Contribution

It presents a novel covariant formulation of worldline numerics for charge dynamics, applicable to high-intensity laser fields, and demonstrates its effectiveness with known analytic solutions.

Findings

Successfully solves Lorentz and Landau-Lifshitz equations numerically.

Maintains explicit covariance and mass-shell condition.

Validates method with analytic plane wave solutions.

Abstract

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.