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Renormalization group theory, the epsilon expansion and Ken Wilson as I knew him

Michael E. Fisher

Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-8510, USA

https://doi.org/10.1142/S0217979215300066Cited by:1 (Source: Crossref)

Abstract

The tasks posed for renormalization group theory (RGT) within statistical physics by critical phenomena theory in the 1960's are set out briefly in contradistinction to quantum field theory (QFT), which was the origin for Ken Wilson's concerns. Kadanoff's 1966 block spin scaling picture and its difficulties are presented; Wilson's early vision of flows is described from the author's perspective. How Wilson's subsequent breakthrough ideas, published in 1971, led to the epsilon expansion and the resulting clarity is related. Concluding sections complete the general picture of flows in a space of Hamiltonians, universality and scaling. The article represents a 40% condensation (but with added items) of an earlier account: Rev. Mod. Phys.70, 653–681 (1998).

This article will also appear in a Ken Wilson Memorial — Renormalization, Lattice Guage Theory, the Operator Product Expansion and Quantum Fields, eds. B. E. Baaquie, K. Huam, M. E. Peskin and K. K. Phua, to be published by World Scientific Publishing Company, 2015.

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