As a first example an antiferromagnet has 2 goldstone bosons, a ferromagnet has 1 goldstone bosons, where in both cases we are breaking symmetry from SO(3) to SO(2), for the antiferromagnet the dispersion is E ∝ ∝ p and the expectation value of the ground state is zero, for the ferromagnet instead the dispersion is E ∝ ∝ p 2 and the expectation value of the ground state is not zero, i.e. there is a spontaneously broken symmetry for the ground state