In particle and condensed matter physics, Goldstone bosons (also known as Nambu-Goldstone bosons) are bosons that appear in models with spontaneously broken symmetry. The Goldstone bosons correspond to the broken symmetry generators -- they can be thought of as the excitations of the field in the symmetric "directions" -- and are massless if the spontaneously broken symmetry is not also broken explicitly. If the symmetry is not exact, i.e., if it is explicitly broken as well as spontaneously broken, then the Goldstone bosons are not massless, though they typically remain light; these are called pseudo-Goldstone bosons or pseudo-Nambu-Goldstone bosons (abbreviated PNGBs). Particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. ... Jeffrey Goldstone is a theoretical physicist and an emeritus physics faculty at MIT. He was educated at the Cambridge University. ... Yoichiro Nambu (1921–) is a Japanese-born American physicist. ... Boson (game) Bosons, named after Satyendra Nath Bose, are particles which form totally-symmetric composite quantum states. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some Lie group goes into a vacuum state that is not symmetric. ... Pseudo-Goldstone bosons arise in a quantum field theory with an approximate symmetry such that if the symmetry were exact, then there would be spontaneous symmetry breaking (SSB) and the consequent formation of Goldstone bosons. ...

Goldstone's theorem

Goldstone's theorem states that whenever a continuous symmetry is spontaneously broken, new massless (or light, if the symmetry was not exact) scalar particles appear in the spectrum of possible excitation. It was first formulated by Jeffrey Goldstone. There is one scalar particle - called a Goldstone boson - for each generator of the symmetry that is broken, i.e., that does not preserve the ground state. Sphere symmetry group o. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... For the quantum mechanical scalar field theory which is a field theory of spinless particles, see Scalar field (physics) Scalar field theory (SWT) is a set of fringe theories in a model which posits that there is a basic mechanism that produces the electric field and the magnetic field. ... Jeffrey Goldstone is a theoretical physicist and an emeritus physics faculty at MIT. He was educated at the Cambridge University. ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ...

There is a slight loophole in the theorem. If you read the theorem carefully, it only states that there exist non-vacuum states with arbitrarily small energies. Take for example a chiral N=1 super QCD model with a nonzero squark VEV which is conformal in the IR. The chiral symmetry is a global symmetry which is (partially) spontaneously broken. Some of the "Goldstone bosons" associated with this SSB are charged under the unbroken gauge group and hence, these composite bosons have a continuous mass spectrum with arbitrarily small masses but yet there is no Goldstone boson with exactly zero mass. In other words, the Goldstone bosons are infraparticles. In quantum field theory, the vacuum state, usually denoted , is the element of the Hilbert space with the lowest possible energy, and therefore containing no physical particles. ... The initialism QCD can mean: Quantum chromodynamics Quintessential Player, formerly known as Quintessential CD Quality, Cost, Delivery, A three-letter acronym used in lean manufacturing This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... In particle physics, a squark is a hypothetical boson partner of a quark whose existence is implied by supersymmetry. ... Wikipedia does not yet have an article with this exact name. ... A conformal field theory is a quantum field theory (or statistical mechanics model) that is invariant under the conformal group. ... Look up ir in Wiktionary, the free dictionary. ... In quantum field theory, a global symmetry is any symmetry of a model which is not a gauge symmetry. ... Elementary particles An elementary particle is a particle with no measurable internal structure, that is, it is not a composite of other particles. ... A mass spectrum is an intensity vs. ... In electrodynamics and quantum electrodynamics, in addition to the global U(1) symmetry related to the electric charge, we also have position dependent gauge transformations. ...

In theories with gauge symmetry, the Goldstone bosons are "eaten" by the gauge bosons. The latter become massive and their new, longitudinal polarization is provided by the Goldstone boson. Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Gauge bosons are bosonic particles which act as carriers of the fundamental forces of Nature. ... The term, longitudinal means front-to-back or top-to-bottom as opposed to transverse which means side-to-side. In automotive engineering, the term, longitudinal refers to an engine in which the crankshaft is oriented along the long axis of the vehicle, front to back. ...

A simple example

We have a complex scalar field φ (phi), with the constraint that φ^*φ=k². One way to get a constraint of that sort is by including a potential In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = −1. ... For the quantum mechanical scalar field theory which is a field theory of spinless particles, see Scalar field (physics) Scalar field theory (SWT) is a set of fringe theories in a model which posits that there is a basic mechanism that produces the electric field and the magnetic field. ... This article needs to be cleaned up to conform to a higher standard of quality. ... It has been suggested that this article or section be merged with Scalar potential. ...

and taking the limit as λ goes to infinity. The field can be redefined to give a real scalar field (i.e., a spin-zero particle) θ without any constraint by using In mathematics and physics, a scalar field associates a scalar to every point in space. ...

where θ is the Goldstone boson (actually kθ is) with the Lagrangian density given by: A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a functional of the dynamical variables which concisely describes the equations of motion of the system. ...

Note that the constant term m²k² has no physical significance and the other term is simply the kinetic term for a massless scalar. In general the Goldstone boson is always massless, and parametrises the curve of possible vacuum states.

Nonrelativistic theories

A version of Goldstone's theorem also applies to nonrelativistic theories (and also relativistic theories with spontaneously broken Lorentz symmetry). It basically states that for each spontaneously broken global symmetry, there corresponds a quasiparticle with no energy gap (the nonrelativistic version of the mass gap). However, two different spontaneously broken generators may give rise to the same Goldstone boson. For example, in a superfluid, both the U(1) particle number symmetry and Galilean symmetry are spontaneously broken. However, the phonon is the Goldstone boson for both. Wikisource has original text related to this article: Relativity: The Special and General Theory Albert Einsteins theory of relativity, or simply relativity, refers specifically to two theories: special relativity and general relativity. ... In physics, Lorentz symmetry is the invariance of physical laws under the Lorentz transformations. ... In physics, a quasiparticle refers to a particle-like entity arising in certain systems of interacting particles. ... In solid state physics and related applied fields, the band gap (or energy gap) is the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. ... A quantum field theory model is said to have a mass gap if the energy spectrum not including zero has a positive greatest lower bound. ... Superfluidity is a phase of matter characterised by the complete absence of viscosity. ... In mathematics, the unitary group of degree n over the field F (which is either the field R of real numbers or the field C of complex numbers) is the group of n by n unitary matrices with entries from F, with the group operation that of matrix multiplication. ... The Galilean transformation is used to transform between the coordinates of two coordinate systems in a constant relative motion in Newtonian physics. ... Normals modes of vibration progression through a crystal. ...

In fact, in general, the phonon is the Goldstone boson for spontaneously broken Galilean/Lorentz symmetry. Galileans (or Galilæans) were members of a fanatical sect (Zealots), followers of Judas of Galilee, who fiercely resented the taxation of the Romans, and whose violence contributed to induce the latter to vow the extermination of the whole race. ...

Goldstone fermions

Spontaneously broken global fermionic symmetries, which occur in some supersymmetric models, lead to Goldstone fermions, or Goldstinos. The bosonic superpartners of the Goldstinos, called sgoldstinos, also appear. This article or section is in need of attention from an expert on the subject. ... Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. ... The goldstino is a Goldstone fermion produced by the spontaneous breaking of supersymmetry. ... Sgoldstino is the proposed superpartner of goldstino. ...

Goldstone bosons in nature

• In fluids, the phonon is longitudinal and it is the Goldstone boson of the spontaneously broken Galilean symmetry. In solids, the situation is more complicated; the Goldstone bosons are the longitudinal and transverse phonons and they happen to be the Goldstone bosons of spontaneously broken Galilean, translational and rotational symmetry with no simple one-to-one correspondence between the Goldstone modes and the broken symmetries.
• In magnets, the original rotational symmetry (present in the absence of an external magnetic field) is spontaneously broken such that the magnetization points into a specific direction. The Goldstone bosons then are the magnons, i.e. spin waves in which the local magnetization direction oscillates.
• The pions are the pseudo-Goldstone bosons that result from the spontaneous breaking of the chiral flavor symmetry of QCD caused by quark condensation. The symmetry is also explicitly broken by the masses of the quarks, so that the pions are not massless.
• The longitudinal polarization components of the W and Z bosons correspond to the Goldstone bosons of the spontaneously broken electroweak symmetry. Because the symmetry is gauged, the Goldstone bosons are "eaten" by the gauge bosons corresponding to the broken generators; this gives the gauge bosons a mass and the associated necessary third polarization degree of freedom. This is achieved in the Standard Model through the Higgs mechanism.

A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. ... Normals modes of vibration progression through a crystal. ... In jewelry, a solid gold piece is the alternative to gold-filled or gold-plated jewelry. ... Iron filings in a magnetic field generated by a bar magnet A magnet is an object that has a magnetic field. ... In particle physics, pion (short for pi meson) is the collective name for three subatomic particles: π0, π+ and π−. Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force. ... Pseudo-Goldstone bosons arise in a quantum field theory with an approximate symmetry such that if the symmetry were exact, then there would be spontaneous symmetry breaking (SSB) and the consequent formation of Goldstone bosons. ... In physics, the W and Z bosons are the elementary particles that mediate the weak nuclear force. ... The Higgs mechanism, originally discovered by the British physicist Peter Higgs (building on a previous suggestion by Philip Anderson in condensed matter physics), is the mechanism that gives masses to all elementary particles in particle physics. ...

See also

• Pseudo-Goldstone boson
• Majoron
• Higgs mechanism
• Mermin-Wagner theorem