The Mass-shift Method and the Self-action of Classical Charge
  The complex non-local action functional is used in classical electrodynamics to describe the back-reaction effects for the charge moving in the constant homogeneous electromagnetic field. We apply the mass-shift method to obtain the higher order radiation effects in the non-relativistic cyclotron motion and generalize the method to the case of Bargmann-Michel-Telegdi particle. 
S.L.Lebedev