CHAPTER 20 - Spontaneous symmetry breaking

Abstract

This chapter explains the W-boson masses by means of the Higgs mechanism of spontaneous breaking of local SU(2) symmetry. Spontaneous symmetry breaking is a result of the degeneracy of the vacuum. The chapter presents several simpler examples of spontaneous breaking of various symmetries—discrete, global and local U(l), and global SU(2). With regard to the spontaneous breaking of discrete symmetry, it can be concluded from the observed data on the expansion of the universe that the vacuum energy density is unlikely to be larger than the observed density of matter. The choice of a specific vacuum is decided by microscopic perturbations in the first moments of the life of the universe. But after the system has spontaneously slipped into one of the vacua, it cannot change into another one. The spontaneous breaking of a continuous global symmetry produces Goldstone bosons. The spontaneous symmetry breaking results in a redistribution of fields—one of the two real fields forming the complex scalar field transforms into the third component of the vector particle, which is transformed from a massless two-component Maxwell photon into a massive three-component Proca boson. As a result of the spontaneous breaking of gauge symmetry, the magnetic field gains a mass whose inverse value characterizes the depth of field penetration into the superconductor. A description of this phenomenon is given by the Ginzburg–Landau equation. The notion of spontaneous symmetry breaking has its genesis in statistical physics.