Symmetry Breaking

Abstract

We want to study the typical behavior of physical fields near a ground state (also called vacuum). It happens frequently that the ground state of a many-particle system is not unique. In this case, the system can oscillate near different ground states which, as a rule, corresponds to different physical behavior. Therefore, the choice of the ground state plays a crucial role. Historically, Pauli criticized the formulation of gauge field theories by Yang and Mills in 1954; Pauli emphasized that the corresponding interacting gauge particles are massless, in contrast to physical experiments. This defect of gauge theories could be cured in the 1960s by using the so-called Higgs mechanism which equips the gauge bosons with mass. This way, the W ^±-bosons and the Z ⁰-boson obtain their mass in the Standard Model of particle physics. Physicists speak of symmetry breaking (or loss of symmetry) for the following reason.

• The original theory possesses a family of ground states which can be transformed into each other by using the symmetry group $\mathcal{G}$ of the theory.

• In nature, physical systems oscillate frequently near a distinguished ground state. These realistic states are not anymore symmetric under the original symmetry group $\mathcal{G}$. In this sense, the symmetry group $\mathcal{G}$ is broken.