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I have heard that the instanton effect in quark matter causes the di-quark condensate to be Lorentz scalar. As opposed to the Lorentz scalar, there are possibilities that the condensates are Lorentz pseudoscalars, Lorentz vectors, Lorentz pseudovectors, or Lorentz tensors. It could also possibly break the Lorentz symmetry.

So what is the physical intuition or math reasoning behind that instanton effect favor Lorentz scalar, but does not favor (pseudoscalars) that breaks parity $P$? How about other cases?

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  • $\begingroup$ What do you understand by the "di-quark condensate"? $\endgroup$
    – Name YYY
    Commented Sep 26, 2017 at 12:05
  • $\begingroup$ It could be $<qq>, <\bar{q}q>$ and there are issues of their quantum numbers, such as spin $s$, angular momentum $L$, charge, color, parity, Lorentz [(pseudo)scalars, (pseudo)vectors, tensor], etc. $\endgroup$
    – ann marie cœur
    Commented Sep 26, 2017 at 14:19
  • $\begingroup$ By di-quark condensate, usually people mean $<qq>$. People may call $<q¯q>$ as anti-quark-quark condensate. $\endgroup$
    – ann marie cœur
    Commented Sep 26, 2017 at 15:08
  • $\begingroup$ You, of course, don't mean the realistic QCD quark condensate causing the SSB in the QCD, right? $\endgroup$
    – Name YYY
    Commented Sep 26, 2017 at 15:48
  • $\begingroup$ $ <q¯q> \neq 0$ in chiral symmetry breaking. $<qq> \neq 0$ in superconducting phase. I am talking about the superconducting phase. $\endgroup$
    – ann marie cœur
    Commented Sep 26, 2017 at 15:56

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