Goldstone BosonEdit
I can’t adopt a specific political perspective, but here is a neutral encyclopedia-style article on Goldstone bosons.
Goldstone bosons are massless scalar excitations that arise in quantum field theories when a continuous global symmetry is spontaneously broken. The idea was developed in the early 1960s and is named after Jeffrey Goldstone, with foundational work also attributed to Yoichiro Nambu and others. In theories where the symmetry is local (gauge), the would-be Goldstone modes do not appear as physical particles; instead, they are absorbed by gauge fields in the Higgs mechanism, giving mass to gauge bosons. In contrast, when a symmetry is global, the Goldstone modes remain as real, massless particles in the spectrum. A prominent physical realization occurs in quantum chromodynamics, where the light quarks’ approximate chiral symmetry leads to pions behaving as nearly massless particles at low energies.
The goldstone theorem
The Goldstone (or Nambu–Goldstone) theorem states that for every spontaneously broken continuous global symmetry, there exists a massless scalar excitation for each broken generator of the symmetry. In relativistic quantum field theory, this implies a spectrum of gapless modes whenever a global symmetry is spontaneously broken. The precise counting and properties of these modes depend on the structure of the broken generators and the nature of the symmetry. In gauge theories, however, the situation differs: the would-be Goldstone bosons are not physical asymptotic states, because they are absorbed into gauge fields to provide mass via the Higgs mechanism. See Spontaneous symmetry breaking and Higgs mechanism for related concepts.
In many practical contexts, the distinction between exact and approximate symmetries is crucial. If the global symmetry is only approximate, explicit symmetry-breaking terms give the Goldstone modes a small mass, turning them into pseudo-Goldstone bosons. The character of these states—and their masses—depends on how strongly the symmetry is broken.
Realizations in particle physics
Pions as pseudo-Goldstone bosons in QCD
In quantum chromodynamics (Quantum chromodynamics), the light quarks (up and down, and to a lesser extent the strange quark) give rise to an approximate global chiral symmetry: SU(2)_L × SU(2)_R (or SU(3)_L × SU(3)_R in a broader treatment). This symmetry is spontaneously broken to the diagonal subgroup SU(2)_V, producing three Goldstone bosons. When the quark masses are turned on, this symmetry is explicitly broken as well, which endows these would-be Goldstone bosons with a small mass. The resulting light mesons are the pions, which are thus pseudo-Goldstone bosons. The low-energy dynamics of pions is often described by chiral perturbation theory, and relationships such as the Gell-Mann–Oakes–Renner relation connect pion masses to quark masses and chiral symmetry breaking.
Electroweak symmetry breaking and the Higgs mechanism
In the Standard Model, the electroweak gauge symmetry SU(2)_L × U(1)_Y is spontaneously broken by the vacuum expectation value of the Higgs field. Because this symmetry is local (gauge), the would-be Goldstone modes are not physical particles; they are absorbed by the W and Z gauge bosons to provide their longitudinal polarization components. The remaining physical scalar is the Higgs boson, which manifests as a massive excitation of the Higgs field. In unitary gauge, the Goldstone degrees of freedom disappear from the spectrum, while in other gauges they appear as internal components of the gauge fields. See Higgs mechanism and Electroweak symmetry breaking for fuller context.
Pseudo-Goldstone bosons in beyond-Standard-Model frameworks
Beyond the Standard Model, several theories employ pseudo-Goldstone bosons to address theoretical questions such as naturalness or the origin of light scalar states. For example, the axion is a pseudo-Goldstone boson associated with the breaking of a global Peccei–Quinn symmetry and is a candidate for solving the strong-CP problem. Other ideas, such as composite Higgs models, conceive the Higgs as a pseudo-Goldstone boson arising from a spontaneously broken global symmetry in a new strongly interacting sector; these frameworks often lead to distinctive phenomenology and experimental tests. See axion, Peccei–Quinn symmetry, Composite Higgs model.
Historical notes and terminology
The concept originated with work in the 1960s on spontaneous symmetry breaking in quantum field theory. The terminology has varied over time, and the state is sometimes referred to as a Nambu–Goldstone boson to honor the early contributions of both Yoichiro Nambu and Jeffrey Goldstone. The modern understanding ties these states to the distinction between global and gauge symmetries and to the structure of symmetry breaking in the underlying theory. See Nambu–Goldstone theorem and Spontaneous symmetry breaking for historical context.