= Gaussian momentum-shell scaling
{c}
{title2=$r'=b^2r,\quad h'=b^{(D+2)/2}h$}
After integrating a free-field momentum shell, restore the cutoff with $x'=x/b$ and $\phi'(x')=b^{(D-2)/2}\phi_<(bx')$. The <gradient> coefficient is invariant, the mass changes as $r'=b^2r$, and a uniform conjugate field changes as $h'=b^{(D+2)/2}h$. This follows by counting measure, derivative and field factors in the quadratic <Hamiltonian>. A nonuniform source instead obeys $h'(x')=b^{(D+2)/2}h(bx')$, with the source on the right projected onto the retained <Fourier modes>. The field has <engineering dimension> $(D-2)/2$ and zero <anomalous dimension>.
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