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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 ℒeff 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:

This resemblance suggests Wilson’s physical reinterpretation of the renormalization procedure. Rather than considering a model’s classical Lagrangian, such as ℒ of Equation (1View Equation), 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.


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