Feynman's linear divergence problem

First, we consider generalized wave and scattering operators and derive modifications of commutation relations (between scattering operators and unperturbed operators) when the corresponding deviation factors behave as $\exp \{it{\mathcal{C}}_{\pm }\}$ for $t\to \pm \mathrm{\infty }$. Then, we construct so called secondary generalized scattering operators for the related case of linear divergence in QED, which gives a positive answer (in that case) to the well-known problem of J. R. Oppenheimer regarding scattering operators in QED: “Can the procedure be freed of the expansion in $\epsilon$ and carried out rigorously?”