The Origins of Lattice Gauge Theory

1
The Origins of Lattice Gauge Theory

• Kenneth G. Wilson
• The Ohio State University

2
The Origins of Lattice Gauge Theory

• 1974 - 2004 Homage
• 1973 - 1974 Origins
• 1958 - 1971 Thesis and After
• 2004 - Research Questions

3
I. 1974 - 2004 Homage

• Current knowledge vs. 1974
• The next thirty years
• Thirty years a long time?
• How about 2700 years?

4
II. 1973 - 1974 Origins (1)

• 1973 Asymptotic Freedom
• I have a problem
• Solution try a lattice
• Confinement?

5
II. 1973 - 1974 Origins (2)

• Summer Formalism clear
• Orsay talk
• Strong coupling

6
II. 1973 - 1974 Origins (3)

• Another problem
• Months of struggle
• Confinement!

7
II. 1973 - 1974 Origins (4)

• Prior experience with lattices, critical
  phenomena
• The Ising Model
• A field theorists laboratory

8
II. 1973 - 1974 Origins (5)

• Retrospective
• A Discovery Waiting to Happen

9
III. 1958 - 1971 Thesis and After (1)

• 1958 Topic (Gell-Mann)
• 1-d Integral equation
• I become irrelevant to Physics (1958-1969)

10
III. 1958 - 1971 Thesis and After (2)

• Learning computing
• Unexpected discovery
• Gell-Mann and Low
• Feynman anecdotes

11
III. 1958 - 1971 Thesis and After (3)

• In my own world
• Theorists laboratories for Strongly Coupled
  Field Theories
• Computers (someday)?

12
III. 1958 - 1971 Thesis and After (4)

• A laboratory experiment
• Butchering a Field Theory
• Momentum Slices
• 1 lt k lt 2, 1000 lt k lt 2000

13
III. 1958 - 1971 Thesis and After (5)

• New Renormalization Group
• Solving Field Theory Slice by Slice
• Number of couplings per step
• Infinite

14
III. 1958 - 1971 Thesis and After (6)

• Two Payoffs!
• Critical Phenomena - A New Expansion
• The Kondo Problem - RG, Slices, solved by
  Computer
• Adjacent Slices

15
III. 1958 - 1971 Thesis and After (7)

• A blunder
• A bizarre episode

16
IV. 2004 - Research Questions

• Colored partners for the gluon
• An RG Infrared Limit Cycle in altered QCD?
• New expansions???

17
The Origins of Lattice Gauge TheorySome
Historical References

• Andrew Pickering Constructing Quarks
• Lillian Hoddeson, et.al., The Rise of the
  Standard Model
• The Dibner Institute for the History of Science
  and Technology Web Site in preparation

18
References for the Two Payoffs

• The Renormalization Group and Critical Phenomena
  II Phase Cell Analysis of Critical Behavior,
  K.G. Wilson, Phys. Rev. B4, 3184 (1971)
• Critical Exponents in 3.99 Dimensions,
  M.E.Fisher and K.G. Wilson, Phys. Rev. Lett. 28,
  240 (1972)

19
References for the Two Payoffs

• Feynman Graph Expansion for Critical Exponents,
  K. G. Wilson, Phys. Rev. Lett. 28, 548 (1971)
• The Renormalization Group Critical Phenomena
  and the Kondo Problem, K.G. Wilson, Rev. Mod.
  Phys. 47, 773-840 (1975)