2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51631The 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.latex, 9 pages, 2 figures, Sc3conf.sty, to appear in Proceedings of 3-d Sakharov ConferenceHigh Energy Physics - Theorytext