Radiation reaction for a massless charged particle

We derive effective equations of motion for a massless charged particle coupled to the dynamical electromagnetic field with regard to the radiation back reaction. It is shown that unlike the massive case, not all the divergences resulting from the self-action of the particle are Lagrangian, i.e., can be cancelled out by adding appropriate counterterms to the original action. Besides, the order of renormalized differential equations governing the effective dynamics turns out to be greater than the order of the corresponding Lorentz-Dirac equation for a massive particle. For the case of a homogeneous external field, the first radiative correction to the Lorentz equation is explicitly derived via the reduction of order procedure.