Parity transformation of a Dirac field
= Parity transformation of a Dirac field
{title2=$\psi'(t,\mathbf x)=\eta_P\gamma^0\psi(t,-\mathbf x)$}
With the mostly-minus <Minkowski metric>, $|\eta_P|=1$ and the usual <Dirac adjoint>, this transformation makes $\bar\psi\psi$ even and $\bar\psi\gamma^5\psi$ odd under <parity>. The latter sign follows from anticommutation of $\gamma^0$ and $\gamma^5$ and does not depend on whether the convention includes an imaginary unit in $\gamma^5$.