Higgs and Goldstone modes in crystalline solids

Optical and acoustic phonons play a central role in solid-state physics. Acoustic phonons can be thought of either as Goldstone bosons, which arise from the breaking of the translational invariance, or as gauge bosons within a non-Abelian gauge theory framework. Nevertheless, optical phonons are left out. Spontaneous symmetry breaking provides a unified framework in which optical and acoustic phonons appear together. After a general overview of this subject, the concept was applied specifically to crystalline phase transitions. Goldstone and Higgs modes arise naturally as a result of spontaneous breaking of a global, continuous crystal symmetry and can be identified with acoustic and optical phonons, respectively.