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Interchanging positions of Gell-Mann matrices with Dirac matrices, Pauli matrices

Add indices to all matrices. The only thing you should then worry about is whether they are real or Grassmann numbers.
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How do you multiply a 4x1 spinor by a $SU(3)$ matrix?

Color and Dirac/spinor indices are different types of indices. E.g. the quark field carries both.
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Is gauge covariant derivative an ordinary covariant derivative?

Whether space-time symmetries (as in GR) or internal symmetries (as in Yang-Mills) are gauged, covariant derivatives are defined such that $D_\mu U(g) X = U(g) D_\mu X$. To get a feel for this, I ...
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Is gauge covariant derivative an ordinary covariant derivative?

The gauge covariant derivative is a genuine covariant derivative in the ordinary sense of differential geometry, but in the general sense of a (principal) connection form $A$ inducing covariant ...
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BRST Symmetry and Single Particle States

I will post an answer because I have understood things in a certain way and I would like to share it. In this way, if it is wrong, I will get to know why it is wrong (if someone is kind enough to ...
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BRST Symmetry and Single Particle States

It isn't obvious from that transformation alone. Remember that in P&S, the forward and backward polarization vectors are defined as: \begin{equation} \epsilon ^{\pm}_{\mu} = \frac{1}{\sqrt{2} |\...
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Conservation of gauge charge

For $SU(N)$, the non-abeliean current density $j_\mu^a$ has $N^2-1$ components (ignoring the spacetime index), the same as the number of generators of the gauge group (which in turn are associated ...
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