ABSTRACT
At the end of Ch. 14, we saw that we want some kind of gauge symmetry associated with vector bosons in order that the theory is renormalizable. The problem that comes with it is the mass of the vector boson, which ought to vanish as a consequence of gauge symmetry. In this chapter, we will discuss some scenarios where the consequences of a symmetry are not realized on the physical observables. Such a phenomenon can happen because of a feature of the ground state of the system, and is called spontaneous symmetry breaking.
In this section, we present several examples of spontaneous symmetry breaking. First, a general comment. If spontaneous symmetry breaking occurs due to the expectation value of a vector field, the ground state must prefer a certain direction in spacetime, which would mean a breaking of Lorentz invariance as well. The same is true if, instead of a vector field, any non-trivial representation of the Lorentz group is used. We want to deal with Lorentz invariant theories. In this case, we can consider non-trivial ground state configuration for scalar fields only. All examples that we present in this section contain only scalar fields.
