# Order Parameter in a Gauge Theory, Can we find one in a Gauge Theory(like QCD)?

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1. Oct 14, 2014

### pedroall

Hello Community!
I can't find a good answer(if there is) to my question.
When in statistical mechanics we can define the order parameter for to study some phase transition. we need to define a order parameter.
Now, I want to know if we can to define/find some "order parameter" for to study the phase transition in a Gauge Theory, for example, in QCD, which is a Gauge Theory and there we have different phase transition.
Then, a Order Parameter in a Gauge Theory: Can we find/define one in a Gauge Theory(like QCD)???
I hope some comment.
Thank you!

2. Oct 17, 2014

### Einj

I am not 100% sure but I am confident that two possible order parameters for QCD are the quark and gluon condensate, i.e. the following expectation values: $\langle 0|q\bar q|0\rangle$ and $\langle 0|F^a_{\mu\nu}F^{\mu\nu}_a|0\rangle$. These expectation values on the vacuum state are usually non-zero and determine, for example, the mass of the pion. The fact that they are non-zero is also closely related to confinement (see for example the MIT bag model). If I remember correctly, at sufficiently high temperature/density the might vanish again, indicating a change from a confined to a deconfined phase (see for example the Quark-Gluon-Plasma).

This is pretty well explained in Yagi book "Quark-Gluon-Plasma: From Big Bang to Little Bang".

I hope this is useful.

3. Oct 17, 2014

### jfy4

For pure gauge, one can use the Wilson loop.

4. Oct 23, 2014

### pedroall

5. Oct 23, 2014

### pedroall

How do you say "..use Wilson loop"?. Sorry, but, only I know which the Wilson loop it's a great criterion for confinement. The idea which I know it's a very and basic aplication of Wilson. Can you tell me some example or reference please? thank you!

6. Oct 25, 2014

### jfy4

You want the expectation value of the Wilson Loop, $\langle W \rangle = \text{Tr}[W e^{iS}]$. Perhaps the best way to work is to switch to a lattice regularization and visualize the Wilson Loop on a 3d lattice and see how it gives information about confinement through its perimeter and area.