A situation in which the lowest-energy state of a many-body system or vacuum state of a relativistic quantum field theory has a lower symmetry than the equations defining the system. Examples in solid-state physics include ferromagnetism, antiferromagnetism, and superconductivity. In particle physics, the Weinberg–Salam model (see electroweak theory) is an important example of a relativistic quantum field theory with broken symmetry.
A result associated with broken symmetry is Goldstone's theorem. This states that a relativistic quantum field theory having continuous symmetry that is broken must include the existence of massless particles called Goldstone bosons. In many-body theory Goldstone bosons are collective excitations. An exception to Goldstone's theorem is provided in the case of broken gauge theories, such as the Weinberg–Salam model, in which the Goldstone bosons become massive bosons known as Higgs bosons. In many-body theory, long-range forces provide the analogous exception to Goldstone's theorem, with the Higgs bosons being excitations with a nonzero gap. Such Higgs bosons are found in superconductors.