= Characteristic solution of the massless Callan-Symanzik equation
{title2=$G_n(\lambda(\mu),\mu)=e^{-n\int_{\mu_0}^{\mu}\gamma_\phi(\lambda(\nu))\,d\nu/\nu}G_n(\lambda_0,\mu_0)$}
For fixed external momenta, the massless <Callan-Symanzik equation> is $(\mu\partial_\mu+\beta(\lambda)\partial_\lambda+n\gamma_\phi)G_n=0$. Choose a <running coupling> satisfying $d\lambda/d\log\mu=\beta(\lambda)$ and $\lambda(\mu_0)=\lambda_0$. The <chain rule> reduces the equation along this curve to $dG_n/d\log\mu=-n\gamma_\phi G_n$, whose integrating factor gives the displayed solution. The reference <correlation function> at $\mu_0$ supplies boundary data; the <renormalization group> alone does not determine these data.
If $\beta=b\lambda^2$, then $\lambda(\mu)=\lambda_0/[1-b\lambda_0\log(\mu/\mu_0)]$. If in addition the <anomalous dimension> is $\gamma_\phi=c\lambda^2$, the integral in the exponent is $(c/b)(\lambda(\mu)-\lambda_0)$. These formulas use the stipulated truncated <renormalization group> functions and apply on a branch on which the running solution remains defined.
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