An Introduction to Gauge Theories

  • Maurice Levy
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 39)


All lectures on gauge theories start with a discussion of the reasons why these theories have been the subject of so much interest in the last seven or eight years. On the one hand, these justifications are less and less necessary as time goes on; on the other, the reasons are changing. To respect to this tradition, I shall list briefly a few of the recent achievements of gauge theories:
  • The success of quantum electrodynamics (QED), the first gauge theory (or the second, if one wants to consider Einstein’s theory of gravitation as a particular gauge theory).

  • The unification of weak and electromagnetic interactions, using Yang-Mills fields (1), and the various predictions which came out of it, particularly the existence of neutral currents.

  • The proof of the renormalizability of massive gauge theories (abelian and non abelian).

  • The predictions of massless gauge theory of strong interactions (chromodynamics), particularly asymptotic freedom and, perhaps, confinement.

  • The possibility to unify strong interactions with the others (weak and electromagnetic).

  • The development of supersymetric theories, and recent progresses in the theory of super-gravity.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C.N. Yang and R.C. Mills, Phys. Rev. 96, 191 (1954).ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    See, for example, S. Abers and B.W. Lee, Physics Reports 9C, n°1 (1973).ADSCrossRefGoogle Scholar
  3. 3.
    R. Gastmans, in Weak and Electromagnetic Interactions at High Energies (Cargèse 1975), Part A, pp. 109–171, Plenum Press (1976).Google Scholar
  4. 4.
    See, for example, J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields (McGraw Hill, 1965 ) pp. 19–20.zbMATHGoogle Scholar
  5. 5.
    P.W. Higgs, Phys. Letters 12,132 (1964). Several other authors could be quoted here: see Ref. 3.ADSCrossRefGoogle Scholar
  6. 6.
    G. ’t Hooft and M. Veltman, Particle interactions at very high energies (part B) pp. 177–322, Plenum Press (1974).Google Scholar
  7. 7.
    G. ’t Hooft, Nucl. Phys. B33, 173 (1971); B35, 167 (1971), G. ’t Hooft and M. Veltman, Nucl. Phys. B50, 318 (1972).ADSCrossRefGoogle Scholar
  8. 8.
    B.W. Lee, Phys. Rev. D5 823 (1972); B.W. Lee and J. Zinn-Justin, Phys. Rev. D5, 3121 (1972); D5, 3137 (1972); D5 3155 (1972); D7, 1049 (1973).ADSGoogle Scholar
  9. 9.
    C. Becchi, A. Rouet and R. Stora, Commun. Math. Phys. 42, 127 (1975).ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    J.C. Ward, Phys. Rev. 78, 1824 (1950); Y. Takahashi, Nuovo Cimento 6, 370 (1957).Google Scholar
  11. 11.
    A.A. Slavnov, Theor. Math. Phys. 10, 99 (1972); J.C. Taylor, Nucl. Phys. B33, 436 (1971).CrossRefGoogle Scholar
  12. 12.
    R. Brandt, Nucl. Phys. B116, 413 (1976).ADSCrossRefGoogle Scholar
  13. 13.
    G. ’t Hooft and M. Veltman, Nucl. Phys. B44, 189 (1972).ADSCrossRefGoogle Scholar
  14. 14.
    R.A. Brandt, Ng Wing-Chiu and K. Young, Phys. Rev. D, to be published.Google Scholar
  15. 15.
    M. Lévy, Nucl. Phys. 57, 152 (1964).CrossRefGoogle Scholar
  16. 16.
    J.C. Pati and A. Salam, Phys. Rev. 10D, 275 (1974).ADSGoogle Scholar
  17. 17.
    J. Schwinger, Ann. Phys. (N.Y.) 2, 407 (1958); M. Gell-Mann and M. Levy, Nuovo Cimento 16, 705 (1960).CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Maurice Levy
    • 1
  1. 1.Laboratoire de Physique Théorique et Hautes EnergiesUniversité Pierre et Marie CurieParisFrance

Personalised recommendations