Radiation reaction and renormalization in classical electrodynamics of a point particle in any dimension

The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived.