The theorem in relativistic quantum field theory that if there is an exact continuous symmetry of the Hamiltonian or Lagrangian defining the system, and this is not a symmetry of the vacuum state (i.e. there is broken symmetry), then there must be at least one spin-zero massless particle, called a Goldstone boson. In the quantum theory of many-body systems Goldstone bosons are collective excitations such as spin waves. An important exception to Goldstone’s theorem is provided in gauge theories with the Higgs mechanism, whereby the Goldstone bosons gain mass and become Higgs bosons. The theorem is named after Jeffrey Goldstone (1933– ).