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A critical history of renormalization by Kerson Huang in 2013

Abstract

Lorentz’s theory of radiation damping

perturbative QED

Wilson’s formulation

Polchinski’s functional equation

Applications to “triviality” and dark energy

1. Dedication

Wilson: the idea that scale determines the perception of the world seems obvious; what is nontrivial is to formulate this fact mathematically, as a physical theory

The focus in this critique is on the applications of renormalization theory to particle physics as opposed to critical phenomena

2. Lorentz: Electron self-force and radiation damping

What is the electron made of?

Lorentz considered it as a uniform charge distribution of radius \[a\] held together by as yet unknown forces

Coulomb forces do not cancel out due to retardation giving rise to a “self-force” and Coulomb interactions give rise to a “self-mass”

The self-mass diverges linearly when \[a \rightarrow 0\] which was the first identification of the so-called “ultraviolet catastrophe”

3. The triumph of QED

4. Dyson: subtraction = multiplication, or the magic of perturbative renormalization

5. Gell-Mann and Low: It’s all a matter of scale

6. Asymptotic freedom

7. The renormalization group (RG)

8. The Landau Ghost

9. Renormalizability

10. Wilson’s renormalization theory

11. In the space of all possible Lagrangians

12. Polchinski’s functional equation

13. Why triviality is not a problem

14. Asymptotic freedom and the Big Bang

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