Radiated power and radiation-reaction force: A derivation based on Fourier transforms

On making use of the Fourier transforms, general formulas for the time-averaged radiated power and radiation-reaction force are obtained in terms of either the spectral distribution of the source current density or the source charge and current density at the retarded time. The former expressions are particularly suited for the derivation of the Lienard formula for the radiated power as well as the Abraham-Becker form of the radiation-reaction force for a pointlike charge. The procedure of getting instantaneous radiation quantities from the corresponding time-averaged ones is discussed critically and the Abraham-Lorentz force, obtained on the basis of the Heaviside-Feynman fields, is identified as the instantaneous radiation-reaction force