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This paper uses elementary techniques drawn from renormalization theory toderive the Lorentz-Dirac equation for the relativistic classical electron fromthe Maxwell-Lorentz equations for a classical charged particle coupled to theelectromagnetic field. I show that the resulting effective theory, valid forelectron motions that change over distances large compared to the classicalelectron radius, reduces naturally to the Landau-Lifshitz equation. Nofamiliarity with renormalization or quantum field theory is assumed.

The Lorentz-Dirac and Landau-Lifshitz equations from the perspective of modern renormalization theory