General principles common to all analytic renormalization techniques

1 General principles common to all analytical renormalization techniques 

Because of these renormalizations, the physical quantities are no longer expressed in terms of the bare parameters of the system but in terms of new physical parameters which are observables. 

When the cut-off tends to zero, the renormalization factors, which in field theory are not observables, become infinite on the contrary, the renormalized system remains finite, and this property enables us to find relations between the various observable physical quantities. 

In each case, renormalizability has to be proved and the proof is generally made in the framework of perturbation theory. For instance, the electromagnetic theory and the Landau-Ginzburg theory are renormalizable,16,17 in this sense, for d = 4. In a similar way, it is not difficult to show that for d 4, the Landau-Ginzburg theory is renormalizable with respect to short-range divergences. 

In another connection, we explicitly showed in Chapter 10 that, in polymer theory, for d 4, it is possible to construct a theory independent of any short-range cut-off. In fact, we started from a regularized theory, introducing a cut-off area s (Chapter 10, Section 1), and we explained how a simple 

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