It has been suggested that this article or section be merged with fermionic condensate. (Discuss)

A chiral condensate (also called fermion condensate or quark condensate) is an order parameter for chiral symmetry breaking in a theory with massless fermions. In a theory with one or more chiral fields, labelled ψ_α with a chiral flavour symmetry relating the fields, if the vacuum expectation value is nonzero, then we say a chiral condensate has formed. Wikipedia does not have an article with this exact name. ... It has been suggested that this article or section be merged with fermion condensate. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... In quantum field theory the vacuum expectation value (also called condensate) of an operator is its average, expected value in the vacuum. ...

Examples

The BCS theory

The BCS theory of superconductivity has a fermion condensate. A pair of electrons in a metal, with opposite spins can form a scalar bound state called a Cooper pair. Then, the bound states themselves form a condensate. Since the Cooper pair has electric charge, this fermion condensate breaks the electromagnetic gauge symmetry of a superconductor, giving rise to the wonderful electromagnetic properties of such states. BCS theory successfully explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without resistance. ... A magnet levitating above a high-temperature superconductor (with boiling liquid nitrogen underneath) demonstrates the Meissner effect. ... Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... Hot metal work from a blacksmith In chemistry, a metal (Greek: Metallon) is an element that readily forms ions (cations) and has metallic bonds, and metals are sometimes described as a lattice of positive ions (cations) in a cloud of electrons. ... The term scalar is used in mathematics, physics, and computing basically for quantities that are characterized by a single numeric value and/or do not involve the concept of direction. ... In physics, a bound state is a composite of two or more building blocks (particles or bodies) that behaves as a single object. ... BCS theory successfully explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without resistance. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ...

QCD

In Quantum chromodynamics (QCD) the chiral condensate is also called the quark condensate. This property of the QCD vacuum is partly responsible for giving masses to hadrons (along with other condensates like the gluon condensate). Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). ... The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). ... In Quantum chromodynamics (QCD), the gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to certain hadrons. ...

In an approximate version of QCD, which has vanishing quark masses for N_f flavours, there is an exact chiral flavour symmetry of the theory. The QCD vacuum breaks this symmetry to SU(N_f) by forming a quark condensate. The quark condensate is therefore an order parameter of transitions between several phases of quark matter in this limit. 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... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). ... In physics, a phase transition is the transformation of a thermodynamic system from one phase to another. ... Quark Matter refers to any of a number of phases of matter built out of quarks and gluons. ...

This is very similar to the BCS theory of superconductivity. The Cooper pairs are analogous to the pseudo-scalar mesons. However, the vacuum carries no charge. Hence all the gauge symmetries are unbroken. Corrections for the masses of the quarks can be incorporated using chiral perturbation theory. BCS theory successfully explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without resistance. ... BCS theory successfully explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without resistance. ... Scalar is a concept that has meaning in mathematics, physics, and computing. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ... Chiral perturbation theory is an effective field theory constructed on a lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics. ...

Helium-3 superfluid

A helium-3 atom is a fermion and at very low temperatures, they form two-atom molecules which are bosonic and condense. Helium-3 is a non-radioactive and light isotope of helium. ... Superfluidity is a phase of matter characterised by the complete absence of viscosity. ... Helium-3 is a non-radioactive and light isotope of helium. ... Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. ...

NOTE: They don't form molecules, but Cooper pairs. The size of these pairs is larger than the interatomic separation. Therefore, the two atom picture is not adequate.

Other models

• A simpler model showing similar phenomena is the Schwinger model.
• See Technicolor models for another example of this kind.
• Nambu-Jona-Lasinio model
• Gross-Neveu model

In physics, the Schwinger model, named after Julian Schwinger, is the model describing 2D (2 spatial 1 time) Euclidean quantum electrodynamics with a Dirac fermion. ... Technicolor models are theories beyond the Standard Model (sometimes, but not always, GUTs) which do not have a scalar Higgs field. ... In quantum field theory, the Nambu-Jona-Lasinio model is a theory of interacting Dirac fermions with chiral symmetry. ... The Gross-Neveu model is a quantum field theory model of Dirac fermions interacting via four fermion interactions. ...

See also

• Superconductivity and the BCS theory.
• The QCD vacuum and the gluon condensate.
• Quark matter, diquark condensate and the pion condensate.
• The top quark condensate and Technicolor models.