Manifest covariant color superconductivity?

Question

@JiaYiyang wrote:

I think color-superconductivity would count. Although the formalism treating it is often not manifestly covariant (which is not surprising since e.g. it's often dealt with in thermal QFT context),  it's still a QCD phenomenon after all.

How can it be manifest? Doesn't the permanent presence of matter always break Lorentz covariance?

Comments

I have not seen a completely manifest covariant treatment. The question is why bother?

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@JiaYiyang Well, since you only wrote ''often'' I concluded that you seem to have treatments in mind where covariance is manifest.  

Why bother? Since in the context of your remark that I cited covariance is essential (though not necessarily manifest covariance). But it seems to me that there is no covariance since matter always defines a preferred frame. 

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 Well, since you only wrote ''often'' I concluded that you seem to have treatments in mind where covariance is manifest.  

Sorry for the confusion, I wrote "often" simply to be safe, just in case there is actually a covariant treatment out there I haven't seen. 

The difference between color-superconductivity and ordinary electron-superconductivity is that the dynamics is treated relativistically (because it's often high-density that is discussed), so in expressions such as $\langle q q\rangle$, the $q$ is still relativistically quantized. But the thermal state certainly breaks manifest covariance. (Aside: maybe I should also say, another difference is that in color-superductivity there's an obvious channel for pairing, i.e. color-Coulomb interaction, which is a plain QCD effect; while in normal electron superconductivity, the pairing mechanism is much subtler, i.e. phonon exchange. In this sense, color-superconductivity theory is much closer to QCD than electron-superconductivity to QED.)

In any case, we know physically when evaluating (thermal-sense) color-condensate such as $\langle qq \rangle$ there is a contribution from the true vacuum, so the true vacuum vev has to be defined.