Solution (source code)

= Solution

A momentum-shell <renormalization group> step has three parts:

1. Split $\phi=\phi_<+\phi_>$ into slow modes $|k|<\Lambda/\zeta$ and fast modes $\Lambda/\zeta<|k|<\Lambda$, then integrate out $\phi_>$ using a <cumulant expansion> to obtain a <Wilsonian effective action> for $\phi_<$.
2. Rescale momenta by $k'=\zeta k$, equivalently coordinates by $x'=x/\zeta$, restoring the cutoff from $\Lambda/\zeta$ to $\Lambda$.
3. Rescale the field by $\phi'(x')=\zeta^{(d-2)/2}\phi_<(x)$ at the <Gaussian fixed point>, restoring the normalized kinetic term.

The resulting functional has the original form and cutoff but new masses and couplings. Iteration produces a <renormalization-group flow>.