PhyAmateur
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Was reading how do vectors transform under chiral transformation and found the following:
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 $$\bar{\psi}\gamma^\mu\psi$$ ?
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 $$\bar{\psi}\gamma^\mu\psi$$ ?