Feynman s struggle and Dyson s surprise revelation

Transcription

1 Feynman s struggle and Dyson s surprise revelation Inconspicuous but fundamental revisions to the foundations of quantum electrodynamics through the development of an appropriate means of representation Feynman ca Dyson 1949 Adrian Wüthrich, University of Bern HQ3, 1 July 2010, Berlin

2 1 Introduction: genesis, modern application and interpretation of Feynman diagrams 2 Feynman s struggle for a physical interpretation of the Dirac equation Feynman s programme Quivering electron Positrons and interaction Abandoning the microscopic model 3 Dyson s systematization and theoretical update Renormalization Removal of divergences through appropriate representation

3 Genesis, modern application and interpretation of Feynman diagrams

4 e e + e + e

5 e e + e + e

6 e e + e + e

7 Feynman rules Peskin and Schroeder 1995, pp

8 Received view Not a representation of a physical process

9 Received view Not a representation of a physical process Invention of a system of abbreviations

10 Received view Not a representation of a physical process Invention of a system of abbreviations No modifications to the physical content Brown (1996): Illustration and Inference; Schweber (1994): QED; Dyson (1965): Nobel Prize

11 Light-by-light scattering Compton scattering Electron scattering off a potential Euler 1936 Heitler 1944 Koba & Takeda 1949 Karplus 1950 Peskin & Schroeder 1995 Peskin & Schroeder 1995

12 Feynman s struggle for a physical interpretation of the Dirac equation

13 Los Alamos badge photos from Welton 2007

14 Feynman s programme I am engaged now in a general program of study I want to understand (not just in a mathematical way) the ideas in all branches of theor. physics. As you know I am now struggling with the Dirac Eqn. Feynman to Welton 1947

15 Of course, the hope is that a slight modification of one of the pictures will straighten out some of the present troubles. Feynman to Welton 1947

16 Zitterbewegung

17 The one dimensional Dirac Eqn. ψ 1 t + ψ 3 z = iµψ 1 ψ 3 t + ψ 1 z = +iµψ 3 Hψ = φψ + α(p A)ψ βµψ No details of the manuscript page may be shown online until copyright clearance F = i(hf FH) + F t ẋ = α (Breit 1928, Schrödinger 1930, Dirac 1933, 1935)

18 No details of the manuscript page may be shown online until copyright clearance New Variables

19 New Variables P ψ L b = Mǫ No details of the manuscript page may be shown online until copyright clearance 0 ψ R a = Nǫ

20 New Variables P ψ L b = Mǫ No details of the manuscript page may be shown online until copyright clearance 0 ψ R a = Nǫ Solve by path counting ψ L (P) = iǫ + (iǫ) 3 MN + (iǫ) 5 M2 2! N 2 2!...

21 New Variables P ψ L b = Mǫ No details of the manuscript page may be shown online until copyright clearance 0 ψ R a = Nǫ Solve by path counting ψ L (P) = iǫ + (iǫ) 3 MN + (iǫ) 5 M2 2! Green s function N 2 2!...

22 Positrons and interaction

23 No details of the manuscript page may be shown online until copyright clearance

24 No details of the manuscript page may be shown online until copyright clearance any completely closed loop cancels

25 No details of the manuscript page may be shown online until copyright clearance

26 No details of the manuscript page may be shown online until copyright clearance this stinks

27 Abandoning the microscopic model

28 Wheeler and Feynman 1949 Space-Time Approach to QED (Feynman 1949)

29 Dyson s systematization and theoretical update

30 Freeman Dyson at Princeton, From

31 The S Matrix in QED (Dyson 1949)

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36 S F S F = Z 2 S F1(e 1 ) D F D F = Z 3 D F1(e 1 ) γ µ Γ µ = Z 1 1 Γ µ1 (e 1 ) Renormalization

37 Removal of divergences through appropriate representation The surprising feature of the S matrix theory, as outlined in this paper, is its success in avoiding difficulties. Starting from the methods of Tomonaga, Schwinger and Feynman, and using no new ideas or techniques, one arrives at an S matrix from which the well-known divergences seem to have conspired to eliminate themselves. This automatic disappearance of divergences is an empirical fact, which must be given due weight in considering the future prospects of electrodynamics. The S Matrix in QED (Dyson 1949, p. 1754)

38 Acknowledgements: Gerd Graßhoff, Tilman Sauer Reference: Adrian Wüthrich (Sept. 2010): The Genesis of Feynman Diagrams. Archimedes Series, Dordrecht: Springer