Kenneth Wilson — Renormalization and QCD

Kenneth Wilson had an enormous impact on field theory, in particular on the renormalization group and critical phenomena, and on QCD. I had the great pleasure to work in three fields to which he contributed essentially: Critical phenomena, gauge-invariance in duality and QCD, and flow equations and similarity renormalization.

Skeleton graph expansion of critical exponents in "cultural revolution" years

Kenneth Wilson's Nobel Prize winning breakthrough in the renormalization group theory of phase transition and critical phenomena almost overlapped with the violent "cultural revolution" years (1966–1976) in China. An unexpected chance in 1972 brought the author of these lines close to the Wilson–Fisher ϵ-expansion of critical exponents and eventually led to a joint paper with Lu Yu published entirely in Chinese without any English title and abstract. Even the original acknowledgment was deleted because of mentioning foreign names like Kenneth Wilson and Kerson Huang. In this article I will tell the 40-year old story as a much belated tribute to Kenneth Wilson and to reproduce the essence of our work in English. At the end, I give an elementary derivation of the Callan–Symanzik equation without referring to field theory.