Goldstone boson

In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu in particle physics within the context of the BCS superconductivity mechanism, and subsequently elucidated by Jeffrey Goldstone, and systematically generalized in the context of quantum field theory. In condensed matter physics such bosons are quasiparticles and are known as Anderson–Bogoliubov modes. These spinless bosons correspond to the spontaneously broken internal symmetry generators, and are characterized by the quantum numbers of these. They transform nonlinearly (shift) under the action of these generators, and can thus be excited out of the asymmetric vacuum by these generators. Thus, they can be thought of as the excitations of the field in the broken symmetry directions in group space—and are massless if the spontaneously broken symmetry is not also broken explicitly. If, instead, the symmetry is not exact, i.e. if it is explicitly broken as well as spontaneously broken, then the Nambu–Goldstone bosons are not massless, though they typically remain relatively light; they are then called pseudo-Goldstone bosons or pseudo–Nambu–Goldstone bosons (abbreviated PNGBs). Goldstone's theorem examines a generic continuous symmetry which is spontaneously broken; i.e., its currents are conserved, but the ground state is not invariant under the action of the corresponding charges. Then, necessarily, new massless (or light, if the symmetry is not exact) scalar particles appear in the spectrum of possible excitations. There is one scalar particle—called a Nambu–Goldstone boson—for each generator of the symmetry that is broken, i.e., that does not preserve the ground state. The Nambu–Goldstone mode is a long-wavelength fluctuation of the corresponding order parameter. By virtue of their special properties in coupling to the vacuum of the respective symmetry-broken theory, vanishing momentum ("soft") Goldstone bosons involved in field-theoretic amplitudes make such amplitudes vanish ("Adler zeros").