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The Renormalization Group

Authors: Michael Stone;

The Renormalization Group

Abstract

The renormalization group was discovered in relativistic field theories by Stuckleberg, and independently by Gell-Mann and Low. Later Leo Kadanoff understood that something similar to the field theory renormalization group was the origin of universality in critical phenomena. It was Ken Wilson who, in a series of papers in the early 1970s, showed how to reconcile the continuum field theory and lattice statistical mechanics viewpoints and made the renormalization group into a practical tool for calculation. It is fair to say that Kadanoff and Wilson changed our entire attitude to quantum field theory. Before them field theory consisted of the Feynman rules for writing down the perturbation expansion, and the renormalization program for extracting finite answers from the divergent Feynman integrals. There was no clear notion of what a field theory was outside perturbation theory. Because the perturbation series is at best an asymptotic expansion, and because such expansions do not uniquely determine the quantity they represent, there was no agreement as to what constituted a valid computation of any nonperturbative effect. People of equal skill and good faith could come to very different conclusions. This is not true today.

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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