Our First Model

The primary target of the book are graduate students; the minimum background required is to have taken a first course on quantum field theory. This chapter aims at readers who have already taken such a course but have not heard about spontaneous symmetry breaking yet. Using a simple toy model, the text explains what spontaneous symmetry breaking is and why it implies the presence of massless particles in the spectrum. Furthermore, it is shown that these Nambu–Goldstone bosons tend to interact weakly at low energies. This simple setting also serves as a primer on some more advanced aspects of field theory. These include the invariance of the S-matrix under field redefinitions, and the construction of effective field theory for Nambu–Goldstone bosons.