NambuGoldstone

Nambu-Goldstone refers to massless excitations that arise when a continuous global symmetry is spontaneously broken in a quantum system. The concept emerged from Goldstone’s theorem, formulated in 1961, and was developed further by Yoichiro Nambu, whose work linked spontaneous symmetry breaking in fermionic systems to particle physics. When a continuous global symmetry is not realized in the vacuum, the low-energy spectrum contains one massless scalar particle for each broken symmetry generator. In relativistic quantum field theories this leads to a spectrum of Goldstone bosons, whose number typically matches the number of broken generators.

If the symmetry is exact but gauged, the Goldstone modes are not physical particles; instead they are absorbed by gauge fields through the Brout-Englert-Higgs mechanism, providing mass to gauge bosons while removing massless scalars from the observable spectrum. When the symmetry is approximate or explicitly broken, the resulting modes acquire a small mass and are referred to as pseudo-Goldstone bosons. This concept helps explain light mesons such as pions in quantum chromodynamics, which are pseudo-Goldstone bosons of approximate chiral symmetry breaking.

In condensed matter physics, similar ideas apply and the corresponding excitations are often called Nambu-Goldstone modes. Examples include phonons from broken translational symmetry and magnons from broken spin-rotation symmetry. The counting and nature of NG modes can vary between relativistic and nonrelativistic systems, with subtleties in some contexts leading to more or fewer gapless modes than the number of broken generators.

Overall, Nambu-Goldstone phenomena describe how continuous symmetries shape the low-energy structure of physical theories and materials.