= Antifermion sign of a normal-ordered bilinear
{title2=$:\bar\psi\Gamma\psi:\supset-d^\dagger d\,\bar v\Gamma v$}
In a <Dirac field> mode expansion, the antiparticle contribution to $\bar\psi\Gamma\psi$ first appears with operator order $dd^\dagger$. <Normal ordering> changes it to $-d^\dagger d$ using the fermionic anticommutation relations. Thus its scattering coefficient is $-\bar v_{\rm in}\Gamma v_{\rm out}$. Pair-annihilation and creation terms have the operator orders $db$ and $b^\dagger d^\dagger$. Keeping these orders and a fixed external-state convention determines interference signs, especially between exchange and annihilation graphs in a <Yukawa interaction>.
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