Was reading how do vectors transform under chiral transformation and found the following:(adsbygoogle = window.adsbygoogle || []).push({});

If $$V^\mu$$ is a vector; set $$ V^\mu = \bar{\psi} \gamma^\mu \psi= $$

$$\bar{\psi}\gamma^\mu e^{-i\alpha\gamma^5}e^{i\alpha\gamma^5}\psi =$$

$$\bar{\psi}\gamma^\mu\psi = V^\mu $$

My questions are why is it that vector takes the form $$V^\mu = \bar{\psi}\gamma^\mu\psi$$ and does the same thing apply to $$\partial_\mu$$ I mean is $$\partial_\mu$$ written as $$\bar{\psi}\gamma^\mu\psi$$ ?

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# Vector under Chiral transformation

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