Reduction of order, resummation and radiation reaction

Understand

The Landau-Lifshitz equation is the first in an infinite series of approximations to the Lorentz-Abraham-Dirac equation obtained from `reduction of order'.

• We show that this series is divergent, predicting wildly different dynamics at successive perturbative orders.
• Iterating reduction of order ad infinitum in a constant crossed field, we obtain an equation of motion which is free of the erratic behaviour of perturbation theory.
• We show that Borel-Pad\'e resummation of the divergent series accurately reproduces the dynamics of this equation, using as little as two perturbative coefficients.