The Propagators for Electrons and Positrons

Abstract

In the following we will generalize the nonrelativistic propagator theory developed in the previous chapter to the relativistic theory of electrons and positrons. We will be guided by the picture of the nonrelativistic theory where the propagator G ⁺(x'; x) is interpreted as the probability amplitude for a particle wave originating at the space-time point x to propagate to the space-time point x'. This amplitude can be decomposed as in (1.28) into a sum of partial amplitudes, the nth such partial amplitude being a product of factors illustrated in Fig. 2.1. According to (1.28), the probability amplitude consists of factors that describe the propagation of the particle between the particular scattering events (caused by the interaction V(x)) and when integrated over the space-time coordinates of the points of interaction represent the nth-order scattering process of the particle.