Abstract
We study the problem of a charged particle affected by an external electromagnetic field, adopting the point of view that its evolution is governed by an autonomous ordinary second order system of differential equations on M4 whose acceleration can be expanded into a power series of the charge e and assuming the acceleration satisfies the Lorentz–Dirac equation. Thus, we locate the dynamics of the system in a symplectic structure up to order e3 for external fields satisfying certain weak conditions. This is applied to obtain conserved quantities associated to symmetries of the external field that are also isometries.
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