Charge conjugation of fermion bilinears
= Charge conjugation of fermion bilinears
For <normal ordering> of a <fermion bilinear>, <charge conjugation> sends $\bar\psi\Gamma\psi$ to $\bar\psi(C^{-1}\Gamma C)^T\psi$. In particular the <Dirac current> is odd and the <axial current> is even under <charge conjugation>.