= CPT transformation of Dirac bilinears
{c}
{title2=$\Theta\overline\psi\Gamma\psi\Theta^{-1}$}
For a Hermitian <fermion bilinear>, an <antiunitary operator> implementing <CPT> conjugates numerical coefficients and exchanges particle and antiparticle fields at $-x$. Reordering the <fermions> then gives $\Theta:\overline\psi\Gamma\psi(x):\Theta^{-1}=:\overline\psi\gamma_5\Gamma\gamma_5\psi(-x):$ when $\Gamma^\dagger=\gamma^0\Gamma\gamma^0$. Thus scalar, pseudoscalar and tensor bilinears are even, while vector and axial-vector bilinears are odd. Each derivative contributes another minus sign. The graded reordering is essential; treating <Dirac fields> as commuting quantities gives the wrong transformation.
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