Spontaneously Broken Symmetries

Abstract

In this chapter we present the solution to the problem of mass. It is based on the phenomenon of spontaneous symmetry breaking (SSB). We first give the example of buckling, a typical example of spontaneous symmetry breaking in classical physics. We extract the main features of the phenomenon, namely the instability of the symmetric state and the degeneracy of the ground state. The associated concepts of the critical point and the order parameter are deduced. A more technical exposition is given in a separate section. Then we move to a quantum physics example, that of the Heisenberg ferromagnet. We formulate Goldstone’s theorem which associates a massless particle, the Goldstone boson, to the phenomenon of spontaneous symmetry breaking. In the last section we present the mechanism of Brout–Englert–Higgs (BEH). We show that spontaneous symmetry breaking in the presence of gauge interactions makes it possible for particles to become massive. The remnant of the mechanism is the appearance of a physical particle, the BEH boson, which we identify with the particle discovered at CERN.