Talk:Fermionic condensate
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What happened here? The version from July seems much clearer than the current version. +sj+ 10:48, 6 Sep 2004 (UTC)
These two topics depsite having similar names should only be merged if done in a specific way. The term "fermionic condensate" or "fermion condensate" refers to the condensation of partlicles into a single coherent quantum state at low temperatures. This phrase is most often used in the broad field of Condensed Matter Physics and can refer to the condensation of electrons in a metal to form a superconductor, condensation of He-3 atoms to form a superfluid or recently the condensation of spin 1/2 atoms in dilute gasses. The article entitled "fermionic condensate" addresses these topics pretty well, giving a good broad introduction. The article entitled "fermion condensate" is far more abstract and specialised and doesn´t address the subject in an accessible or broad enough manner for such a forum. In fact not even for a condensed matter specialist.
Having said the above, it is not a satisfactory postion to be in having to so closely named articles. I would suggest adding a section at the bottom of "fermionic condensates" briefly mentioning some of the points from the other article and then if neccessary adding some more specifically named articles addressing the more abstract topics in further detail separately.
In view of the above comments, I have redirected Fermion condensate to this article. Below is the material from Fermion condensate that I either felt was too complex to include in the article, or that I was not qualified to merge in a safe manner. If anyone feels capable, please go ahead and work it in:-
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 ψα with a chiral flavour symmetry relating the fields, if the vacuum expectation value 
is nonzero, then we say a chiral condensate has formed.
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[edit] Examples
[edit] 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.
[edit] 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 Nf flavours, there is an exact chiral flavour 
symmetry of the theory. The QCD vacuum breaks this symmetry to SU(Nf) by forming a quark condensate. 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 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.
[edit] Helium-3 superfluid
A helium-3 atom is a fermion and at very low temperatures, they form two-atom Cooper pairs which are bosonic and condense into a superfluid. These Cooper pairs are substantially larger than the interatomic separation.
[edit] 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
[edit] Re-added some material
I noticed that chiral condensate redirects to this article, but there was no mention of chiral condensates here at all: the article discussed only the recent work on atomic condensates. So I've taken a stab at re-adding the material from the other article given above, with some reduction in sophistication along the way. The article may be a bit repetative now, but at least it's a step closer to being complete. (If you'd rather keep this article focused exclusively on the recent atomic condensate work, then the other material really needs to have its own article, too.) Oh, and I added an expert-needed template, because I don't have the time to do all the necessary cleanup myself (nor expertise in the full range of topics covered).--Steuard 23:45, 26 May 2006 (UTC)
