### 2.7 The meaning of renormalizability

The previous discussion about the cancellation between the cutoffs on virtual light-particle momenta
and the explicit cutoff-dependence of is eerily familiar. It echoes the traditional discussion of the
cancellation of the regularized ultraviolet divergences of loop integrals against the regularization dependence
of the counterterms of the renormalized Lagrangian. There are, however, the following important
differences:
- The cancellations in the effective theory occur even though is not sent to infinity, and even
though contains arbitrarily many terms which are not renormalizable in the traditional
sense (i.e., terms whose coupling constants have dimensions of inverse powers of mass in
fundamental units where ).
- Whereas the cancellation of regularization dependence in the traditional renormalization
picture appears ad-hoc and implausible, those in the effective Lagrangian are sweet reason
personified. This is because they simply express the obvious fact that only was introduced
as an intermediate step in a calculation, and so cannot survive uncancelled in the answer.

This resemblance suggests Wilson’s physical reinterpretation of the renormalization procedure. Rather
than considering a model’s classical Lagrangian, such as of Equation (1), as something pristine and
fundamental, it is better to think of it also as an effective Lagrangian obtained by integrating out still more
microscopic degrees of freedom. The cancellation of the ultraviolet divergences in this interpretation is
simply the usual removal of an intermediate step in a calculation to whose microscopic part we are not
privy.