An Introduction to Lattice Gauge Theories

  • J. Zinn-Justin
Part of the NATO ASI Series book series (NSSB, volume 126)


By studying the renormalized perturbation theory of ordinary continuous gauge theories which corresponds to the classical lagrangian L:
$$ L = \frac{1}{{4g_0^2}}{\vec F_{\mu \nu }}{\vec F_{\mu \nu }},{\vec F_{\mu \nu }} = {\partial _\mu }{\vec A_\nu } - {\partial _\nu }{\vec A_\mu } + {\vec A_\mu } \times {\vec A_\nu }, $$
we learn from renormalized group arguments that the theory is simple at short distance, and complicated at long distance where the effective coupling constant becomes large. Therefore the perturbative spectrum of the theory which consists of massless vector mesons may not be the true spectrum of the theory.


Gauge Theory Partition Function Gauge Transformation Lattice Gauge Theory Saddle Point Equation 


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  1. 1.
    K. Wilson, Phys. Rev. D10 (1974) 2445 and then studied with the use of standard methods of statistical mechanics in.ADSGoogle Scholar
  2. 2.
    R. Balian, J. M. Drouffe, C. Itzykson, Phys. Rev. D10 (1974) 3376.ADSGoogle Scholar
  3. R. Balian, J. M. Drouffe, C. Itzykson, Phys. Rev. D11 (1975) 2098.ADSGoogle Scholar
  4. R. Balian, J. M. Drouffe, C. Itzykson, Phys. Rev. D11 (1975) 2104.ADSGoogle Scholar
  5. 3.
    J. B. Kogut, L. Susskind, Phys. Rev. D11 (1975) 395. Since they have been the subject of a very abundant literature, and thoroughly discussed in various lectures and review articles to which the interested reader will be refered for more details and bibliography.ADSGoogle Scholar
  6. 4.
    Cargèse lectures 1976, M. Levy et al. ed. (Plenum Press, 1977) Cargèse lectures 1979, G.’ t Hooft et al. ed. (Plenum Press, 1980).Google Scholar
  7. 5.
    L. P. Kadanoff, Rev. Mod. Phys. 49 (1977) 267.MathSciNetADSCrossRefGoogle Scholar
  8. 6.
    J. B. Kogut, Rev. Mod. Phys. 51 (1979) 659.MathSciNetADSCrossRefGoogle Scholar
  9. 7.
    J. B. Kogut, Les Houches lectures 1982, J.B. Zuber and R. Stora eds, North Holland to appear.Google Scholar
  10. 8.
    M. Creutz, L. Jacobs, C. Rebbi, Phys. Reports 95 (1983) 20.CrossRefGoogle Scholar
  11. 9.
    J. M. Drouffe and J. B. Zuber, Phys. Reports 102 (1983) 1.MathSciNetADSCrossRefGoogle Scholar
  12. 10.
    C. Rebbi “Lattice gauge theories and Monte Carlo simulations” World Scientific, Singapore 1983.Google Scholar
  13. 11.
    J. Zinn-Justin, Les Houches lecture notes 1982, R. Stora and J.B. Zuber eds., North Holland.Google Scholar
  14. 12.
    E. Brezin and J. Zinn-Justin, Phys. Rev. Lett. 36 (1976) 691.ADSCrossRefGoogle Scholar
  15. E. Brezin and J. Zinn-Justin, Phys. Rev. B14 (1976) 3110.ADSGoogle Scholar
  16. 13.
    J. Zinn-Justin, Cargèse lectures 1973, Saclay preprint.Google Scholar
  17. 14.
    K. Symanzik, Mathematical problems in theoretical physics, Lecture notes in Physics, R. Schroeder et al. eds. (Springer, Berlin, 1982); Improved action in lattice gauge theories, in non-perturbative field theory and QCD, R. Iengo et al. eds (World Scientific, Singapore) 1983 DESY preprints 83/016, 83/026.Google Scholar
  18. 15.
    G. Martinelli, G. Parisi and R. Petronzio, Phys. Lett. 100B (1981) 485.ADSGoogle Scholar
  19. B. Berg, S. Meyer, I. Montvay and K. Symanzik, Phys. Lett. 126B (1983) 467.ADSGoogle Scholar
  20. R. Musto, F. Nicodemi and R. Pettorino, Phys. Lett. 129B (1983) 95.ADSGoogle Scholar
  21. S. Belforte, G. Curci, P. Menotti and G. Paffuti, Phys. Lett. 131B (1983) 423.ADSGoogle Scholar
  22. S. Belforte, G. Curci, P. Menotti and G. Paffuti, Phys. Lett. 136B (1984) 399.ADSGoogle Scholar
  23. B. Berg, A. Billoire, S. Meyer and C. Panagiotakopoulos, Phys. Lett. 133B (1983) 359.ADSGoogle Scholar
  24. P. Weisz, Nucl. Phys. B212 (1983) 1.MathSciNetADSCrossRefGoogle Scholar
  25. G. Curci, P. Menotti and G. Paffuti, Phys. Lett. 130B (1983) 205.ADSGoogle Scholar
  26. F. Gutbrod and I. Montvay, Phys. Lett. 136B (1984) 411.ADSGoogle Scholar
  27. 16.
    E. Brezin, J. C. Le Guillou and J. Zinn-Justin “Phase transitions and Critical Phenomena”, vol. 6, C. Domb and M.S. Green eds. (Academic, 1976) pp. 169-170.Google Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • J. Zinn-Justin
    • 1
  1. 1.CEN - SACLAYGif-sur-Yvette CedexFrance

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