# Vector under Chiral transformation

1. Nov 2, 2014

### PhyAmateur

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 $$\bar{\psi}\gamma^\mu\psi$$ ?

2. Nov 7, 2014