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arXiv · 2105.01640

Reduction of order, resummation and radiation reaction

Robin Ekman·Tom Heinzl·Anton Ilderton
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Abstract

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. Comparing with the Lorentz-Abraham-Dirac equation, our results show that for large times the optimal order of truncation typically amounts to using the Landau-Lifshitz equation, but that this fails to capture the resummed dynamics over short times.

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Robin Ekman, Tom Heinzl, Anton Ilderton. 2021-05-04. Reduction of order, resummation and radiation reaction. https://doi.org/10.1103/physrevd.104.036002

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