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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)