Renormalization Group Theory, the Epsilon Expansion and Ken Wilson as I knew Him

2016 ◽  
pp. 323-366
Author(s):  
Michael E. Fisher
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Renormalization Group Theory ◽  
Epsilon Expansion

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

2015 ◽  
Vol 29 (08) ◽  
pp. 1530006 ◽  
Author(s):  
Michael E. Fisher
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Statistical Physics ◽  
Quantum Field ◽  
Renormalization Group Theory ◽  
Early Vision ◽  
General Picture ◽  
Epsilon Expansion ◽  
Scaling Picture ◽  
Block Spin

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).

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