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is there a numerical algorithm (Numerical methods) to get 'renormalization' ?? i mean you have the action $ S[ \phi] = \int d^{4}x L (\phi , \partial _{\mu} \phi ) $ for a given theory and you want to get it renormalized without using perturbation theory .. can this be made with numerical methods ??

or on the other side let us suppose we have a divergent integral in perturbative renormalization and you want to evaluate it with numerical methods to extract some finite part of it.

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Ken Wilson showed how to do numerical renormalization pretty early on, in Rev. Mod. Phys. 47, 773 (1975). – wsc Sep 3 '12 at 14:21
up vote 3 down vote accepted

The answer to this question is a resounding YES. Lattice field theorists do their computations entirely numerically. As a result, they must resort to numerical (and hence, nonperturbative) renormalization (by extrapolating down the lattice spacing).

They would not deal with counterterms, but rather deal directly with the various $Z$ factors appearing in the renormalized Lagrangian.

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