with a constant prefactor, then the action for the field θ (x) , i.e., the "phase" of the Higgs field Φ(x) , has only derivative terms. This is not a surprise: Adding a constant to θ (x) is a symmetry of the original theory, so different values of θ (x) cannot have different energies. This is an example of configuring the model to conform to Goldstone's theorem : Spontaneously broken continuous symmetries (normally) produce massless excitations.