Our discussion in early chapters captures the spirit of quantum mechanics but is restricted to particles moving along a line. Thats not very unrealistic. In this chapter we breathe some life into quantum particles and allow them to roam in three-dimensional space. This entails an understanding of angular momentum. We will pay particular attention to the hydrogen atom, whose quantum solution was one of the first great triumphs of quantum mechanics and still underlies all of atomic physics.

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.