Renormalization of gauge theories

  • J. Zinn-Justin
New Developments in Quantum Theory
Part of the Lecture Notes in Physics book series (LNP, volume 37)


Gauge Theory Global Symmetry Ward Identity Power Counting Perturbation Series 
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Introduction of non abellian gauge theories

  1. C.N. Yang and R. Mills, Phys. Rev. 96, 191 (1954)CrossRefGoogle Scholar
  2. R. Utiyama, Phys. Rev. 101, 1597 (1956)CrossRefGoogle Scholar
  3. M. Gell-Mann and S. Glashow, Ann. Phys. (N.Y.) 15, 437 (1961)Google Scholar

The quantization has been discussed in

  1. R.P. Feynman, Acta Phys. Polonica 26, 697 (1963)Google Scholar
  2. V.N. Popov and L.D. Faddeev “Perturbation Theory for gauge invariant fields”, Kiev ITP report (unpublished)Google Scholar
  3. L.D. Faddeev and V.N. Popov; Phys. Lett. 25B, 29 (1967)Google Scholar
  4. B. De Witt Phys. Rev. 162, 1195, 1239 (1967)Google Scholar
  5. S. Mandelstam. Phys. Rev. 175, 1580 (1968)CrossRefGoogle Scholar
  6. E.S. Fradkin and I.V. Tuytin, Phys. Lett. 30B, 562 (1969), Phys. Rev. D2, 2841 (1970)Google Scholar
  7. M.T. Veltman, Nucl. Phys. B21, 288 (1970)Google Scholar
  8. G. 't Hooft, Nucl. Phys. B33, 173 (1971)CrossRefGoogle Scholar

The Ward-Takahashi identities were first discussed in

  1. J.C. Ward, Phys. Rev. 78, 1824 (1950)Google Scholar
  2. Y. Takahashi, Nuov. Cim. 6, 370 (1957)Google Scholar

The W.T. identities for the non-abelian gauge theories were first discussed in

  1. A.A. Slavnov, Theor. and Math. Phys. 10, 152 (1972) English translation: Theor. and Math. Phys. 10, 99 (1972)Google Scholar
  2. J.C. Taylor, Nucl. Phys. 10, 99 (1971)Google Scholar

The dimensional regularization for gauge theories was introduced in

  1. G. 't Hooft and M. Veltman, Nucl. Phys. B44, 189 (1972)CrossRefGoogle Scholar

The renormalization of gauge-theories for Green's functions was studied in

  1. B.W. Lee and J. Zinn-Justin, Phys. Rev. D5, 3121, 3137 (1972) and D7, 1049 (1973)Google Scholar
  2. G. 't Hooft and M.T. Veltman, Nucl. Phys. B50, 318 (1972)Google Scholar

W.T. identities for the 1PI generating functional have been obtained in

  1. B.W. Lee, Phys. Lett 46B, 214 (1974) and Phys. Rev. D9, 933 (1974)Google Scholar

The “super-symmetryr” of gauge theories and its use in the derivation of W.T. identities have been outlined in

  1. C. Becchi, A. Rouet and S. Stora, Renormalization of the Higgs-Kibble model (Marseilles preprint,to be published)Google Scholar

This method seems useful in the study of the renormalization of gauge invariant operators

  1. H. Stern-Kluberg and J.B. Zuber, Ward identities and some clues to the renormalization of gauge invariant operators, Saclay preprint D. Ph-T/74-56 (to be published)Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • J. Zinn-Justin
    • 1
  1. 1.Centre d'Etudes Nucléaires de SaclayGif-sur-YvetteFrance

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