Lattice Gauge Theories

  • Marvin Weinstein


In the past few days we have heard several beautiful lectures describing the way in which people hope to extract interesting physical information from quantum field theories by studying their semi-classical versions. Being in the mountains it seems appropriate to describe these attempts as an attack on the semi-classical face of quantum field theory. Since all mountains have more than one face, I would like to describe in my next few lectures attempts which have been made to launch a direct attack on the quantum face (Fig. 1); hence these lectures are in a sense complementary to the preceding ones.


Ising Model Continuum Theory Lattice Theory Lattice Gauge Theory Fermion Theory 
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  1. 1).
    A review of the ideas of Kadanoff and Wilson can be found in “Lectures on the Application of Renormalization Group Techniques to Quarks and Strings”, Leo P. Kadanoff, PRINT-76-0772 (Brown). First of five lectures at University of Chicago, “Relativistically Invariant Lattice Theories”, K.G. Wilson, CLNS-329 (February 1976, Coral Gables Conference); “Quarks and Strings on a Lattice”, K.G. Wilson, CLNS-321 (November 1975, Erice School of Physics); K.G. Wilson and J. Kogut, Phys. Rev. 12, 75 (1974); L.P. Kadanoff, “Critical Phenomena”, Proc. International School of Physics “Enrico Fermi”, Course LI, ed. M. S. Green (Academic, New York, 1972). Thomas L. Bell and Kenneth G. Wilson, “Nonlinear Renormalization Groups”, CLNS-268 (May 1974). For a discussion of the ideas of these authors as applied to more physical models, as well as references to earlier works see T. Banks, S. Raby, L. Susskind, J. Kogut, D.R.T. Jones, P.N. Scharbach and D.K. Sinclair, Phys. Rev. D15, 1111 (1977); J. Kogut, D.K. Sinclair and L. Susskind, Nucl. Phys. B114, 199 (1976); L. Susskind, PTENS 76/1 (January 1976); L. Susskind and J. Kogut, Phys. Reports 23C, 331 (1976).Google Scholar
  2. 2).
    See lectures in this volume for a list of references.Google Scholar
  3. 3).
    C.G. Callan, R. Dashen and D. Gross, “Toward a Theory of Strong Interactions”, Institute for Advanced Study preprint COO-222-115.Google Scholar
  4. 4).
    See J. Kogut, Phys. Rev. 12, 75 (1974) ref. 1 as well as J. Kogut and L. Susskind, Phys. Rev. D11, 395 (1975); L. Susskind, Lectures at Bonn Summer School, 1974 (unpublished); T. Banks, J. Kogut and L. Susskind, Phys. Rev. D13, 1043 (1976).Google Scholar
  5. 5).
    S.D. Drell, M. Weinstein and S. Yankielowicz, Phys. Rev. D14, 487 (1976); D14, 1627 (1976); “Quantum Field Theories on a Lattice: Variational Methods for Arbitrary Coupling Strengths and the Ising Model in a Transverse Magnetic Field”, Stanford Linear Accelerator Preprint SLAC-PUB-1942 (1977), to appear in Phys. Rev.ADSGoogle Scholar
  6. 6).
    Helen R. Quinn and M. Weinstein, “Multiple Vacua in a Lattice Formulation of the Two Dimensional Higgs Model”, SLAC-PUB-2034, submitted to Phys. Rev. D.Google Scholar
  7. 7).
    S.D. Drell, B. Svetitsky and M. Weinstein, “Fermion Field Theory on a Lattice”, SLAC-PUB-1999, to be published in Phys. Rev. D.Google Scholar
  8. 8).
    S. Coleman, Commun. Math. Phys. 31, 259 (1973).ADSMATHCrossRefGoogle Scholar
  9. 9).
    N.D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • Marvin Weinstein
    • 1
  1. 1.Stanford Linear Accelerator CenterStanfordUSA

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