Scattering theory and resonances

Relativistic scattering theory has been generally based on quantum field theory, providing methods of computing an S matrix (transition amplitude operator) by the semi-axiomatic approach of Lehmann et al. (1955) or through the use of interaction picture expansion of the perturbed field equations (Schweber 1964; Jauch and Rohrlich 1955; Schwinger-Tomonaga 1948). Feynman’s approach to scattering in spacetime (Feynman 1949), using the method of propagators, is very close to theCovariant oscillator methods afforded by the covariant quantum theory that we shall discuss below, but the notion of invariant evolution is not used explicitly in those computations (Feynman 1950), however derived Stueckelberg’s equation for free motion of a single particle, and Schwinger (1951) arrived at an evolution equation of Steuckelberg type in his treatment of the propagator in the derivation of the electron anomalous moment, to be discussed in the next chapter).