Pole residue
= Pole residue
{title2=$Z_{\rm pole}=\lim_{p^2\to m^2}(p^2-m^2)G(p)/i$}
The coefficient of a simple one-particle pole in a <propagator> is its pole residue. If $G(p)=i/[p^2-m_0^2-\Sigma(p^2)]$ and $m$ is the <pole mass>, then $Z_{\rm pole}=[1-\Sigma'(m^2)]^{-1}$. An <on-shell renormalization scheme> may impose unit residue by a finite or divergent <wave-function renormalization>; mere <ultraviolet finiteness> does not force the residue to be one.