  The effective Lagrangian of a point charge is derived by eliminating the
electromagnetic field within the framework of the classical closed time path
formalism. The short distance singularity of the electromagnetic field is
regulated by an UV cutoff. The Abraham-Lorentz force is recovered and its
similarity to anomalies is underlined. The full cutoff-dependent linearized
equation of motion is obtained, no runaway trajectories are found but the
effective dynamics shows acausality if the cutoff is beyond the classical
charge radius. The strength of the radiation reaction force displays a pole in
its cutoff-dependence in a manner reminiscent of the Landau-pole of
perturbative QED. Similarity between the dynamical breakdown of the time
reversal invariance and dynamical symmetry breaking is pointed out.
