Question

How would psi_bar gamma_mu psi transform under parity transformation?

Answer 1

$$P( \bar{\psi} \gamma_\mu \psi) =\bar{\psi} \gamma_0 \gamma_\mu \gamma_0 \psi= (\bar{\psi} \gamma_\mu \psi) \epsilon^\mu$$

where

$$\epsilon^\mu =1\space for \space \mu=0 \space and -1\space for \mu = 1,2,3$$