Lagrangian description of the radiation damping

We present a Lagrangian formalism to the dissipative system of a charge interacting with its own radiation field, which gives rise to the radiation damping [W. Heitler, The Quantum Theory of Radiation, third ed., Dover, New York, 1970; J.D. Jackson, Classical Electrodynamics, second ed., Wiley, New York, 1975 (Chapters 14, 17); G.N. Plass, Rev. Mod. Phys. 33 (1961) 37], by the indirect representation doubling the phase-space dimensions.