12 - Scattering, the Scattering Matrix and Cross-Sections

Summary

The majority of our data concerning the particle world comes from scattering experiments, and the theoretical analysis of these is of fundamental importance. This analysis has two parts. First, we encode the properties of the scattering in an object called the S-matrix, whose computation is a main objective of the theory. Second, we relate the S-matrix to quantities that can actually be measured in our laboratory, the so-called cross-sections. We explain heuristically, through the analysis of situations of increasing complexity, what the S-matrix is, but we do not try yet to compute it. We then turn to the relation between the S-matrix and cross-sections, proving that indeed the S-matrix contains the information needed to predict the outcome of these experiments.