QED and the man who didn׳t make it: Sidney Dancoff and the infrared divergence

•I give a history of the infrared divergence leading up to a 1939 paper by S. Dancoff.•I study this paper, which supposedly didn׳t renormalize QED only due to a mistake.•I argue that Dancoff׳s mistake resulted from standard practices of 1930s QED.•I argue that Dancoff was not on the verge of developing renormalized QED in 1939.•I analyze how the supposed importance of Dancoff׳s mistake was later constructed.

Sidney Dancoff׳s paper “On Radiative Corrections for Electron Scattering” is generally viewed in the secondary literature as a failed attempt to develop renormalized quantum electrodynamics (QED) a decade early, an attempt that failed because of a mistake that Dancoff made. I will discuss Dancoff׳s mistake and try to reconstruct why it occurred, by relating it to the usual practices of the quantum field theory of his time. I will also argue against the view that Dancoff was on the verge of developing renormalized QED and will highlight the conceptual divides that separate Dancoff׳s work from the QED of the late 1940s. I will finally discuss how the established view of Dancoff׳s paper came to be and how the reading of this specific anecdote relates to more general assessments of the conceptual advances of the late 1940s (covariant techniques, renormalization), in particular to their assessment as being conservative rather than revolutionary.