Initial-Value Problem for the Non-local Generalization of the Lorentz-Dirac Equation

Although the equation of motion, recently proposed for the classical radiating electron, is of non-local character in proper time, the Newtonian initial data (position and velocity) are sufficient to guarantee existence and uniqueness of the solutions. The corresponding existence proof is accomplished by the Picard-Lindelöf method of successive approximations. This method indicates the possibility of a perturbation expansion of the exact solution in terms of the non-locality parameter. Such a perturbation expansion does not seem to be possible in the Lorentz-Dirac theory.