Editing Fermionic condensate (section)

==Examples==

===Chiral condensate===
A '''chiral condensate''' is an example of a fermionic condensate that appears in theories of massless fermions with [[chiral symmetry]] breaking, such as the theory of quarks in [[Quantum chromodynamics|Quantum Chromodynamics]].

===BCS theory===
The [[BCS theory]] of [[superconductivity]] has a fermion condensate. A pair of [[electron]]s in a [[metal]] with opposite spins can form a [[scalar (physics)|scalar]] [[bound state]] called a [[Cooper pair]]. The bound states themselves then 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 unusual electromagnetic properties of such states.

===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]]).

In an approximate version of QCD, which has vanishing quark masses for ''N'' quark [[flavour (particle physics)|flavour]]s, there is an exact chiral {{nowrap|SU(''N'') × SU(''N'')}} symmetry of the theory. The [[QCD vacuum]] breaks this symmetry to SU(''N'') by forming a quark condensate. The existence of such a fermion condensate was first shown explicitly in the lattice formulation of QCD. The quark condensate is therefore an [[order parameter]] of transitions between several phases of [[quark matter]] in this limit.

This is very similar to the [[BCS theory]] of superconductivity. The [[Cooper pairs]] are analogous to the [[pseudoscalar meson]]s. However, the vacuum carries no charge. Hence all the [[gauge symmetry|gauge symmetries]] are unbroken. Corrections for the masses of the [[quark]]s can be incorporated using [[chiral perturbation theory]].

===Helium-3 superfluid===
A [[helium-3]] atom is a [[fermion]] and at very low temperatures, they form two-atom [[Cooper pair]]s which are bosonic and condense into a [[superfluid]]. These Cooper pairs are substantially larger than the interatomic separation.