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Dec 30, 2017 at 0:17 vote accept user140561
Oct 18, 2017 at 18:20 comment added user140561 @JamalS You're right. I edited the answer to be more precise. Thank you.
Oct 18, 2017 at 18:20 history edited user140561 CC BY-SA 3.0
Included JamalS's remark.
Oct 18, 2017 at 18:10 comment added JamalS $u$ and $\bar u$ are spinors, so they carry $\alpha,\beta$ indices, just as when we write $\gamma^\mu$ we mean $(\gamma^\mu)_{\alpha\beta}$. Two spinors with one $\gamma^\mu$ soaks up the two spinor indices, but we still have the Lorentz index. So while you can swap them safely, strictly speaking the factor on its own is not a scalar unless you are more specific with regards to what it is a scalar with respect to.
Oct 18, 2017 at 18:06 history answered user140561 CC BY-SA 3.0