The last chapter developed the general principles for writing down a relativistic quantum field theory. It showed what types of fields are possible, and explained that spin-one fields can only appear in an interacting, renormalizable theory if they are coupled via the gauge principle.

In this chapter, we write down specifically what the field content of the standard model is. The interactions will then follow as the most general set of renormalizable interactions, compatible with that field content. We then explore what the vacuum and the particle content are, and write down the complete interaction Hamiltonian in the particle basis.

We will not attempt to motivate theoretically why the particle content of the standard model is what it is. We have no deep understanding of why the gauge group is SUc(3) × SUL(2) × UY (1), for instance. We just take the field content as observed fact, and present it. The exception is the Higgs boson, which has not been observed. This is the weakest part of our understanding of the standard model. Note however that the field content of the standard model is not completely arbitrary; once the gauge group is known, the fermionic field content is somewhat constrained by the requirement of anomaly cancellation, which we discuss at the end of the chapter.