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  Instanton effects on condensates: (pseudo)scalars, (pseudo)vectors, tensor

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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?

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart
asked Sep 25, 2017 in Theoretical Physics by annie marie heart (1,205 points) [ no revision ]
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But how this "di-quark condensate" can be the scalar? It is non-invariant by the construction.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user Name YYY
Do you agree that meson is $q¯q$ pair but it can be a pseudo-scalar? In fact, it can be (Pseudo)-scalar/vector meson and Tensor meson. If so what leaves the constraints for writing $qq$, and for writing $q¯q$?

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart
My understanding is that you can insert $\gamma^5$ and $\gamma^\mu$ into the condensate (what it means implicitly in the condensate shorthand).

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart
The condensate itself has nothing to do with the vector, tensor and scalar mesons.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user Name YYY
No, that was not what I mean. The instanton may favor certain channels such that only certein (pseudo)scalars, (pseudo)vectors, tensor tend to condense. I am asking which and what instanton causes this effect, what do they favor others.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart
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By di-quark condensate, usually people mean $<qq>$. People may call $<q¯q>$ as anti-quark-quark condensate.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart
You, of course, don't mean the realistic QCD quark condensate causing the SSB in the QCD, right?

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user Name YYY

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