= Source renormalization of a scalar generating functional
{title2=$h_0=\mu^{-\epsilon/2}Z^{-1/2}h$}
For $d=4-\epsilon$, write the bare field as $\phi_0=Z^{1/2}\phi$ and the renormalized source coupling as $\mu^{-\epsilon/2}h\phi$. In bare variables this is $h_0\phi_0$, with the displayed source. At fixed bare parameters, the source running is $\mu\,d\log h/d\mu=\epsilon/2+\tfrac12\widehat\beta\,\partial_\lambda\log Z$. Normalizing the <generating functional> by its zero-source value cancels source-independent vacuum diagrams and the constant measure factor from field rescaling. It does not remove source-dependent <ultraviolet divergences> or <infrared divergences>; the former require the ordinary field, mass and interaction <counterterms>.
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