The Origins of Lattice The Origins of Lattice Gauge TheoryGauge Theory

Kenneth G. WilsonKenneth G. Wilson

The Ohio State UniversityThe Ohio State University

The Origins of Lattice Gauge TheoryThe Origins of Lattice Gauge Theory

I.I. 1974 - 2004 Homage1974 - 2004 Homage

II.II. 1973 - 1974 Origins1973 - 1974 Origins

III.III. 1958 - 1971 Thesis and After1958 - 1971 Thesis and After

IV.IV. 2004 -2004 - Research Questions Research Questions

I. 1974 - 2004 HomageI. 1974 - 2004 Homage

A.A. Current knowledge vs. 1974Current knowledge vs. 1974

B.B. The next thirty yearsThe next thirty years

C.C. Thirty years: a long time?Thirty years: a long time?

D.D. How about 2700 years?How about 2700 years?

II. 1973 - 1974 Origins (1)II. 1973 - 1974 Origins (1)

A.A. 1973: Asymptotic Freedom1973: Asymptotic Freedom

B.B. I have a problemI have a problem

C.C. Solution: try a latticeSolution: try a lattice

D.D. Confinement?Confinement?

II. 1973 - 1974 Origins (2)II. 1973 - 1974 Origins (2)

A.A. Summer: Formalism clearSummer: Formalism clear

B.B. Orsay talkOrsay talk

C.C. Strong couplingStrong coupling

II. 1973 - 1974 Origins (3)II. 1973 - 1974 Origins (3)

A.A. Another problemAnother problem

B.B. Months of struggleMonths of struggle

C.C. Confinement!Confinement!

II. 1973 - 1974 Origins (4)II. 1973 - 1974 Origins (4)

A.A. Prior experience with lattices, critical Prior experience with lattices, critical phenomenaphenomena

B.B. The Ising Model:The Ising Model:

A field theorist’s laboratoryA field theorist’s laboratory

II. 1973 - 1974 Origins (5)II. 1973 - 1974 Origins (5)

Retrospective:Retrospective:

A Discovery Waiting to HappenA Discovery Waiting to Happen

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

A.A. 1958 Topic (Gell-Mann)1958 Topic (Gell-Mann)

B.B. 1-d Integral equation1-d Integral equation

C.C. I become irrelevant to Physics (1958-I become irrelevant to Physics (1958-1969) 1969)

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

A.A. Learning computingLearning computing

B.B. Unexpected discoveryUnexpected discovery

C.C. Gell-Mann and LowGell-Mann and Low

D.D. Feynman anecdotesFeynman anecdotes

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

A.A. In my own worldIn my own world

Theorist’s laboratories for Strongly Theorist’s laboratories for Strongly Coupled Field TheoriesCoupled Field Theories

B.B. Computers (someday)?Computers (someday)?

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

A.A. A laboratory experiment:A laboratory experiment:

Butchering a Field TheoryButchering a Field Theory

B.B. Momentum SlicesMomentum Slices

1 < k < 2, 1000 < k < 2000 …1 < k < 2, 1000 < k < 2000 …

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

New Renormalization Group:New Renormalization Group:

Solving Field Theory Slice by SliceSolving Field Theory Slice by Slice

Number of couplings per step:Number of couplings per step:

InfiniteInfinite

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

Two Payoffs!Two Payoffs!

Critical Phenomena - A New ExpansionCritical Phenomena - A New Expansion

The Kondo Problem - RG, Slices, solved The Kondo Problem - RG, Slices, solved by Computerby Computer

Adjacent SlicesAdjacent Slices

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

A.A. A blunderA blunder

B.B. A bizarre episodeA bizarre episode

IV. 2004 - Research QuestionsIV. 2004 - Research Questions

A.A. Colored partners for the gluonColored partners for the gluon

B.B. An RG Infrared Limit Cycle in altered An RG Infrared Limit Cycle in altered QCD?QCD?

C.C. New expansions???New expansions???

The Origins of Lattice Gauge TheoryThe Origins of Lattice Gauge TheorySome Historical ReferencesSome Historical References

Andrew Pickering: Andrew Pickering: Constructing QuarksConstructing Quarks

Lillian Hoddeson, et.al.,Lillian Hoddeson, et.al., The Rise of the The Rise of the Standard ModelStandard Model

The Dibner Institute for the History of Science The Dibner Institute for the History of Science and Technology Web Site: in preparationand Technology Web Site: in preparation

References for the Two PayoffsReferences for the Two Payoffs

““The Renormalization Group and Critical The Renormalization Group and Critical Phenomena II: Phase Cell Analysis of Phenomena II: Phase Cell Analysis of Critical Behavior,” K.G. Wilson, Critical Behavior,” K.G. Wilson, Phys. Rev. Phys. Rev. B4B4, 3184 (1971), 3184 (1971)

““Critical Exponents in 3.99 Dimensions,” Critical Exponents in 3.99 Dimensions,” M.E.Fisher and K.G. Wilson, M.E.Fisher and K.G. Wilson, Phys. Rev. Phys. Rev. Lett.Lett. 2828, 240 (1972), 240 (1972)

References for the Two PayoffsReferences for the Two Payoffs

““Feynman Graph Expansion for Critical Feynman Graph Expansion for Critical Exponents,” K. G. Wilson, Exponents,” K. G. Wilson, Phys. Rev. Lett.Phys. Rev. Lett. 2828, 548 (1971), 548 (1971)

““The Renormalization Group: Critical The Renormalization Group: Critical Phenomena and the Kondo Problem,” Phenomena and the Kondo Problem,” K.G. Wilson, K.G. Wilson, Rev. Mod. Phys.Rev. Mod. Phys. 4747, 773-840 , 773-840 (1975)(1975)