Shortly after moving to Berkeley, Weinberg slips a disc and is bedbound. He reads Chandrasekhar’s stellar physics book, which helped spark his interest in astrophysics. They decide to stay on the San Francisco side of the bay. At that time, Berkeley was the world’s leading center of experimental research on elementary particles and the newly commissioned Bevatron was the latest particle accelerator. Weinberg resolves to do some work that will be useful to Berkeley experimenters and sets about studying muon physics. In Spring 1960, he is offered and accepts a tenure-track position as an assistant professor. He is invited to join JASON, the group of defense consultants. He begins teaching and learns that he loves it. He decides to take a year abroad via an Alfred Sloan Fellowship and he and Louise buy a round-the-world ticket.

This chapter gives a brief but quantitative introduction to the method of Feynman diagrams in quantum field theory, sufficient for the reader to understand what these diagrams mean. The concept of “vacuum energy” is discussed in this context.

This chapter introduces how we can use the quantum fields introduced in the previous chapter to access amplitudes and, thus, measurable quantities, such as the cross sections and the particle lifetime. More specifically, an educational tour of quantum electrodynamics (QED), which describes the interaction of electrons (or any charged particles) with photons, is proposed. Although this chapter uses concepts from quantum field theory, it is not a course on that topic. Rather, the aim here is to expose the concepts and prepare the reader to be able to do simple calculations of processes at the lowest order. The notions of gauge invariance and the S-matrix are, however, explained. Many examples of Feynman diagrams and the calculation of the corresponding amplitudes are detailed. Summation and spin averaging techniques are also presented. Finally, the delicate concept of renormalisation is explained, leading to the notion of the running coupling constant.

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.