Renormalization of Gauge Theories

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1. [1] C. Becchi, A. Rouet, R. StoraThe Abelian Higgs Kibble Model, Unitarity of the S OperatorPhys. Lett.52B, 344 (1974). 
2. C. Becchi, A. Rouet, R. StoraRenormalization of the Abelian Higgs Kibble ModelCommun. math. Phys., to be published. 
3. [2] W. ZimmermannAnn. Phys.77, 536 (1973) MR325064
4. W. ZimmermannAnn. Phys.77, 570 (1973) MR325065
5. [3] J. H. LowensteinCommun. math. Phys.24, 1 (1971) Zbl0221.35008MR1552578
6. [4] Y. M. P. LamPhys. Rev. D6, 2145 (1972) 
7. Y. M. P. LamPhys. Rev. D7, 2943 (1973) 
8. M. Bergere, Y. M. P. Lam to be published 
9. [5] H. Epstein, V. Glaser : Ann. Inst. Henri Poincaré, XIX, n° 3, p. 211 (1973) MR342091
10. H. Epstein, V. Glaser : in Statistical Mechanics and Quantum Field Theory. Les Houches Summer School of Theoretical Physics, 1970, Gordon and BreachNew York1971, C. de Witt, R. Stora Ed. Zbl0242.46002
11. H. Epstein, V. Glaser : Colloquium on Renormalization Theory, CNRS, Centre de Physique Théorique, Marseille Juno 1971, CERN TH 1344, June 1971 
12. [6] M. Gomes, J. H. LowensteinPhys. Rev. D7, 550 (1973) 
13. [7] J. H. Lowenstein, B. SchroerPhys. Rev. D7. 1929 (1973) 
14. C. BecchiCommun. math. Phys.33-97 (1973) MR1552599
15. [8] A complete bibliography about the theory of gauge fields can be found for instance in : E. S. Abers, B. V. LeePhys. Reports9C , n° 1 (Nov. 1973) 
16. M. Veltman Invited talk presented at the International Symposium on Electron and Photon Interactions at High Energies, Bonn 2 / - 31, August 1973. 
17. M. Veltman The algebraic structure referred to here is however along the lines of [1]. 
18. M. Veltman The results of the présent paper have been announced by C. Becchi, A. Rouet, R. Stora, CNRS Centre de Physique Théorique, Marseille, Colloquium on Recent Progress in Lagrangian Field Theory, June 1974 and summarized in 
19. J. IliopoulosProgress in gauge théories, Rapporteur's talk, 17th International Conference on High Energy Physics, London1974. 
20. J. Iliopoulos The symmetry property described in [1] is applied to traditional renoraalization procédures in : 
21. J. Zinn JustinLectures given at the International Summer Institute for Theoretical Physics, Bonn 1974. 
22. [9] L. C. Biedenharn in Colloquium on Group Theoretical Methods in Physics. CNRSMarseille June 5-9 (1972) (where however the implications of renormalizability thanks to which all algebraic problems reduce to essentially finite dimensional ones, have not been investigated). 
23. C. M. Lifwtilynn SmithPhys. Lett.468, 233 (1973) and private discussions 
24. J. Wess, B. ZuminoPhys. Lett.378, 95 (1971) MR342064
25. [10] S. L. AdlerPhys. Rev.177, 2426 (1969) Lectures on Elementao Particles and Quantum Field Theory, 1970 Brandeis University Summer Institute of Theoretical Physics, S. Deser, M. Grisaru, H. Pendleton Ed., M.I.T. Press, Cambridge, Mass. 1970 
26. W. BardeenPhys. Rev.184, 1848 (1969) 
27. [11] J. H. Lowenstein, B. SchroerPhys. Rev. D6, 1553 (1972) 
28. [12] J. H. Lowenstein, to be published 
29. C. Becchi, to be published 
30. T. Clark, A. Rouet, to be published 
31. [13] J. H. Lowenstein, W. Zimmermann, to be published 
32. Ph. Blanchard, R. Seneor : CERN/TH 1420 preprint, Nov. 1971CNRS Centre de Physique Théorique Marseille, Colloquium on Renormalization Theory, June 1971, and to be published in Ann. Inst. Henri Poincaré 
33. [14] A. A. SlavnovTMΦ10, 153 (1972) 
34. [15] L. D. Faddeev, V. N. PopovPhys. Lett.25B, 29 (1967) 
35. [16] G. 't HooftNuclear Physics B35, 167 (1971) 
36. G. 't Hooft, H. VeltmanCNRSMarseille, Colloquium on Yang Mills Flelds, June 1972 CERN/TH 1571 
37. [17] Séminaire Sophus Lie, Ecole Normale SupérieureParis1954 : Théorie des Algèbres de Lie. in [9], the relevance of cohomology theory in the présent context can be detected. 
38. [18] G. 't Hooft, M. Veltman CERN Yellow Report TH/73/9 "Diagrammar" (1973) ; 
39. G. 't Hooft, M. VeltmanNuclear Physics B50, 318, (1972). 
40. [19] The treatment of non linear gauges would require the introduction of two more multiplets of external fields, one coupled to the renormalized gauge function, one coupled to the renormalized Slavnov variation of the gauge function, with appropriate dimensions and quantum numbers. cf.Ref[1]. 
41. [20] C. Becchi, A. Rouet, R. Stora Lectures given at the International School of Elementary Particle Physics, Basko Polje, Yugoslavia 14-29 Sept. 1974 and to be published 
42. [21] Using the LSZ formula, it is enough to compute $\partial {𝒵}_c\left(𝒥\right)/\partial \lambda$, $(\lambda =\kappa ,m_{4-\pi }^2)$ and, from the Legendre transform structure of ${𝒵}_c\left(𝒥\right)$. to show that the matrix elements of the gauge function between physical states vanish, as a consequence of the Slavnov identity. More generally, one can check that physical matrix elements of time ordered products of gauge functions are disconnected. 
43. [22] G. 't HooftNuclear Physics, B35, 167 (1971) 
44. [23] The treatment of double poles given in [1] can easily be adapted modulo the modifications due to the non hermiticity of the Lagrangian described here. 
45. [24] The main référence is : "Séminaire Sophus Lie 1. 1954/1955, "Théorie des Algèbres de Lie", Ecole Normale Supérieure, Secrétariat Mathématique, 11, rue Pierre Curie, Paris 5e. Zbl0068.02102
46. A sunmary can be found in N. Bourbaki, Groupes et Algèbres de Lie, Ch. I, §3, Problem n° 12, HermannParis (1960). Zbl0483.22001