Causal Perturbation Theory

Abstract

In this chapter we deal with full QED which means that both the electronpositron field and the radiation field are quantized. In the preceding chapter, in particular in Sect. 2.4, we learned the important lesson that it is very difficult to give a precise meaning to interacting field operators directly. We have to retreat to scattering theory, instead, and we shall now construct the scattering matrix of full QED. The S-matrix maps the asymptotically incoming, free fields on the outgoing ones and, hence, it should be possible to express it by the well-defined free fields. We already emphasized the importance of causality for this purpose (Sects. 2.8–10). Here we shall see causality in its full strength: The S-matrix is essentially completely determined by causality and translation invariance, supposed the coupling, i.e. the first order of the perturbation series, is given.