ABSTRACT
This chapter looks at the ferromagnet and describes the Bogoliubov model for the ground state of a superfluid, which provides an important physical example of a spontaneously broken global Abelian U(1) symmetry. It shows that the excitations away from the ground state are massless modes and shows, via Goldstone’s theorem, that such modes are an inevitable result of spontaneously breaking a global symmetry. The chapter introduces the ‘Goldstone model’ which is the simplest example of a spontaneously broken global U(1) symmetry, involving just one complex scalar field. The generalization of this to the non-Abelian case will draw us in the direction of the Higgs sector of the Standard Model. Returning to condensed matter systems, the chapter introduces the BCS ground state for a superconductor, in a way which builds on the Bogoliubov model of a superfluid.
