In a theory with two chiral fields, ψ1 and ψ2 with a global symmetry relating the relative phases of both fields, but at low temperatures, the correlation function is nonzero, then we say a fermion condensate (also called chiral condensate) has formed. The VEV above is the order parameter. See order-disorder. For example, in QCD, there is an approximate (so there's no real spontaneous symmetry breaking; the VEV will always be aligned in a fixed direction) axial symmetry which is broken because the quarks form a chiral condensate because of a pool of instantons. See Technicolor (physics) for another example. BCS in superconductivity is another.
Heuristically, what happens is a pair of fermion can form a bound state, like a Cooper pair or a meson. Then, the bound states themselves form a condensate. A Cooper pair is not electrically neutral and so, a Cooper pair condensate would necessarily break the electromagnetic gauge symmetry. Similarly, a meson breaks chirality. A phenomological description of the (composite) meson field is given by the chiral model.
To get a "feel" for chiral condensates, a good toy model to start with is the Schwinger model.
It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate.
) chiral flavour symmetry of the QCD Lagrangian is broken in the vacuum state of the theory.
Prototypically, the baryon number of the chiral bag remains an integer, independent of bag radius: the exterior baryon number is identified with the topological winding number density of the Skyrme soliton, while the interior baryon number consists of the valence quarks (totaling to one) plus the spectral asymmetry of the quark eigenstates in the bag.
The earliest recognized fermionic condensate described the state of electrons in a superconductor; the physics of other examples including recent work with fermionic atoms is analogous.
A chiralcondensate is an example of a fermionic condensate that appears in theories of massless fermions with chiral symmetry breaking.
The primary difference between superfluid helium and a Bose-Einstein condensate is that the former is condensed from a liquid while the latter is condensed from a gas.
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