This chapter is devoted to basic aspects of quantum field theory, ranging from the foundations to perturbation theory and renormalization, and is limited to the canonical formalism (functional methods are treated in Chapter 2) and to the traditional workflow (Lagrangian --> Feynman rules --> time-ordered products of fields --> scattering amplitudes) for the calculation of scattering amplitudes (the spinor-helicity formalism and on-shell recursion are considered in Chapter 4).The problems of this chapter deal with questions in scalar field theory and quantum electrodynamics, while non-Abelian gauge theories are discussed in Chapter 3.

Chapter 5 described quantum mechanics in the context of particles moving in a potential. This application of quantum mechanics led to great advances in the 1920s and 1930s in our understanding of atoms, molecules, and much else. But, starting around 1930 and increasingly since then, theoretical physicists have become aware of a deeper description of matter, in terms of fields. Just as Einstein and others had much earlier recognized that the energy and momentum of the electromagnetic field is packaged in bundles, the particles later called photons, so also there is an electron field whose energy and momentum is packaged in particles, observed as electrons, and likewise for every other sort of elementary particle. Indeed, in practice this is what we now mean by an elementary particle: it is the quantum of some field that appears as an ingredient in whatever seem to be the fundamental equations of physics at any stage in our progress.