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

Thank you Einj!! for your comment, I will review your information and read the recomendation.

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.

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