Introduction

Feynman diagrams have long been a staple tool for theoretical physicists. The line drawings were originally developed in the late 1940s by the American physicist Richard Feynman for the perturbative study of quantum electrodynamics, and are taught today to students of quantum field theory in much the same manner as Feynman originally designed them. Yet for a time during the 1950s and 1960s, Feynman diagrams became an equally indispensable tool in the hands of quantum field theory's rivals - particle physicists following the lead of Lev Landau and Geoffrey Chew, who aimed to construct a fully autonomous S-matrix theory built around a scaffolding of Feynman diagrams, but conspicuously lacking all field-theoretic notions of quantum fields or Hamiltonians. By the early 1960s, Chew and his collaborators had commandeered the field-theoretic diagrams while denouncing quantum field theory as being both bankrupt and dead. In the process, Feynman diagrams were re-invested with distinct meanings by the S-matrix theorists, and were taken to represent a fundamentally different basis for studying the constitution and interactions of particles.

There was a series of steps by which S-matrix theorists crafted an autonomous diagrammatic method, some of which we consider here. First came Geoffrey Chew's 1958 particle-pole conjecture. This work was soon extended by Chew in collaboration with Francis Low in their 1959 work on scattering off of unstable targets.