On the divergence difficulty of quantized field theories and the rigorous treatment of radiation reaction

By an orthodox application of the perturbation theory to the general case of a quantized field, it is shown th at the divergence difficulty hitherto encountered arises from a faulty application of the expansion method. The difficulty, in certain cases, disappears if the degeneracy of the unperturbed system is properly treated by the method of secular perturbation. Physically, this amounts to a rigorous treatm ent of the radiation reaction, in such cases where its effect is strong.