The Scattering Matrix in Higher Orders

Abstract

In Chap. 3 many scattering processes were calculated to the lowest nonvanishing order of perturbation theory. Because of the small value of the coupling constant α≈1/137 the first term alone frequently gives reliable results. Within a satisfactory theory, however, one should be able to calculate the contributions of higher orders too. As we shall see in QED – and the same is true in all quantum field theories – this leads to characteristic difficulties: some of the “small corrections” become infinitely large! Surmounting this problem has been an essential step in the development of the theory. In what follows we shall discuss “renormalization in the lowest nontrivial order of perturbation theory. The finite theory obtained in this way can then be applied to calculate measurable effects of vacuum fluctuations, i.e. the interaction with virtually created particles.