  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).
