The state is not abolished, it withers away: how quantum field theory became a theory of scattering

It is described how quantum field theory went from a theory for calculating the properties of stationary states, in the mold of quantum mechanics, to the scattering-focused theory we know today. This development is located as originating in the 1930s and 40s, primarily in the attempts by Werner Heisenberg and Richard Feynman to find a new theory of relativistic quantum mechanics that gets rid of the notion of state entirely. It is then shown how these attempts formed the conceptual inspiration and the provided the formal tools for the formulation of modern, scattering-based QFT in the late 1940s, in particular by Freeman Dyson (and, to some extent, by E.C.G. Stueckelberg). This transformation of quantum field theory is interpreted as a paradigm shift in a weak sense, where the foundations of the theory remain the same, while the paradigmatic problem to be calculated changes (in this case from energy levels to scattering amplitudes).
Comment: This paper was originally published in Studies in the History and Philosophy of Modern Physics, Volume 60 (2017), pp. 46-80. Due to formatting mistakes that appeared only after proof-reading, parts of that paper are garbled. An erratum was published in SHPMP that links to this version, which is the definitive version of the paper