Feynman's linear divergence problem

Abstract

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 $t\to \pm \infty$. 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?"

This work may be considered as a follow up of the paper arXiv:2511.02847, where the logarithmic divergence was studied