Controversies, Letter to Phys. Rev. Lett. and Recollections of S. G. Gasiorowicz

For some years, the conclusion that “at least one of the renormalization constants in quantum electrodynamics is infinite” was generally accepted. In the last paragraph of his [1953c] paper, Kallen had, however, a disclaimer: “The proof presented here makes no pretence at being satisfactory from a rigorous, mathematical point of view. It contains, for example, a large number of interchanges of orders of integrations, limiting processes and so on. From a strictly logical point of view we cannot exclude the possibility that a more singular solution exists where such formal operations are not allowed. It would, however, be rather hard to understand how the excellent agreement between experimental results and lowest order perturbation theory calculations could be explained on the basis of such a solution.”