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Group theory for Feynman diagrams in non-Abelian gauge theories

Predrag Cvitanović*

  • Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305

  • *Present address: Institute for Advanced Study, Princeton, New Jersey 08540. After Oct. 1, 1976; Department of Theoretical Physics, Oxford University, 12 Parks Rd., Oxford OX1-3PQ, England.

Phys. Rev. D 14, 1536 – Published 15 September, 1976

DOI: https://doi.org/10.1103/PhysRevD.14.1536

Abstract

A simple and systematic method for the calculation of group-theoretic weights associated with Feynman diagrams in non-Abelian gauge theories is presented. Both classical and exceptional groups are discussed.

References (75)

  1. J. M. Cornwall and G. Tiktopoulos, Phys. Rev. Lett. 35, 338 (1975) Phys. Rev. D 13, 3370 (1976)
  2. J. J. Carazzone, E. R. Poggio, and H. R. Quinn, Phys. Rev. D 11, 2286 (1975) ibid.12, 3368 (1975) E. R. Poggio and H. R. Quinn, ibid. 12, 3279 (1975)
  3. D. R. T. Jones, Nucl. Phys. B75, 531 (1974)
  4. W. E. Caswell, Phys. Rev. Lett. 33, 244 (1974)
  5. H. T. Nieh and Y.-P. Yao, Phys. Rev. Lett. 32, 1074 (1974) Phys. Rev. D 13, 1082 (1976) C. Y. Lo and H. Cheng, ibid. 13, 1131 (1976)
  6. B. M. McCoy and T. T. Wu, Phys. Rev. D 12, 3257 (1975) ibid.13, 1076 (1976) Stony Brook Report No. ITP-SB-75-49, 1975 (unpublished)
  7. L. Tyburski, Phys. Rev. D 13, 1107 (1976)
  8. L. N. Lipatov, Yad. Fiz. 23, 642 (1976) [Sov. J. Nucl. Phys. (to be published)] V. S. Fadin, E. A. Kuraev, and L. N. Lipatov, Phys. Lett. 60B, 50 (1975)
  9. L. L. Frankfurt and V. E. Sherman, Zh. Eksp. Teor. Fiz. Pis'ma Red. 21, 736 (1975) [JETP Lett. 21, 348 (1975)] L. L. FrankfurtV. E. ShermanYad. Fiz. (to be published)
  10. Y.-P. Yao, Phys. Rev. Lett. 36, 653 (1976)
  11. T. Appelquist, J. Carazzone, H. Kluberg-Stern, and M. Roth, Phys. Rev. Lett. 36, 768 (1976) ibid.36, 1161(E) (1976) A. Mueller (unpublished)
  12. Omitted endnote

  13. D. J. Gross and F. Wilczek, Phys. Rev. D 8, 3633 (1973)
  14. G. Racah, Ergebnisse der Exacten Naturwissenschaften, edited by G. Höhler (Springer, Berlin, 1965), Vol. 37, pp. 28-84
  15. Brian G. Wybourne, Classical Groups for Physicists (Wiley, New York, 1974)
  16. G. 't Hooft, Nucl. Phys. B72, 461 (1974)
  17. G. P. Canning, Phys. Rev. D 12, 2505 (1975) Niels Bohr Inst. Report No. NBI-HE-74-2, 1974 (unpublished) R. F. Cahalan and D. Knight, Phys. Rev. D (to be published)
  18. J. Tits, Ned. Akad. Wetensch. Proc. A69, 223 (1966)
  19. H. Freudenthal, Advan. Math. 1, 145 (1964)
  20. R. D. Schafer, Introduction to Nonassociative Algebras (Academic, New York, 1966)
  21. N. Jacobson, Exceptional Lie Algebras (Dekker, New York, 1971)
  22. F. Gürsey, in Proceedings of the Kyoto Conference on Mathematical Problems in Theoretical Physics, Kyoto, 1975 (unpublished) M. Günaydin, Nuovo Cimento 29A, 467 (1975)
  23. H. Fritzsch, M. Gell-Mann, and H. Leutwyler, Phys. Lett. 47B, 365 (1973) S. Weinberg, Phys. Rev. Lett. 31, 494 (1973)
  24. P. Cvitanović (unpublished)
  25. N. Mukunda and L. K. Pandit, J. Math. Phys. 6, 746 King's College report, 1975 (1965)
  26. L. M. Kaplan and M. Resnikoff, J. Math. Phys. 8, 2194 (1967)
  27. A. J. Macfarlane, A. Sudbery, and P. M. Weisz, Commun. Math. Phys. 11, 77 (1968) Proc. R. Soc. London A314, 217 (1970)
  28. P. Dittner, Commun. Math. Phys. 22, 238 (1971) ibid.27, 44 (1972)
  29. M. A. Rashid and Saifuddin, J. Math. Phys. 14, 630 (1973)
  30. K. J. Barnes and R. Delbourgo, J. Phys. A 5, 1043 (1972)
  31. L. Michel and L. A. Radicati, Ann. Inst. Henri Poincaré 18, 13 (1973)
  32. R. Rockmore, Phys. Rev. D 11, 620 (1975)
  33. A. McDonald and S. P. Rosen, J. Math. Phys. 14, 1006 (1973)
  34. R. E. Cutkosky, Ann. Phys. (N.Y.) 23, 415 (1963)
  35. D. E. Neville, Phys. Rev. 132, 844 (1963)
  36. Omitted endnote

  37. M. Gell-Mann, Caltech Report No. CTSL-20, 1961 M. Gell-Mann and Y. Ne'eman, The Eightfold Way (Benjamin, New York, 1964), p. 11
  38. Canning ([17]) Penrose ([39,40]) J. Mandula (unpublished) Yeung [46]) Cahalan and Knight ([17]) [41]
  39. R. Penrose, in Combinatorial Mathematics and its Applications, edited by D. J. A. Welsh (Academic, New York, 1971), pp. 221-244
  40. T. Murphy, Proc. Camb. Philos. Soc. 71, 211 (1972)
  41. H. Biritz, Nuovo Cimento 25B, 449 (1975) G. P. Canning, Phys. Rev. D 8, 1151 (1973) J. S. Briggs, Rev. Mod. Phys. 43, 189 (1971) H. P. Dürr and F. Wagner, Nuovo Cimento 53A, 255 (1968) V. K. Agrawala and J. G. Belinfante, Ann. Phys. (N.Y.) 49, 130 (1968)
  42. E. M. Andreev, É. B. Vinberg, and A. G. Élashvili, Funct. Analysis and Appl. 1, 257 (1967) E. B. Dynkin, Trans. Amer. Math. Soc. (2) 6, 111 (1957)
  43. J. Patera and D. Sankoff, Tables of Branching Rules for Representations of Simple Lie Algebras (Univ. de Montréal, Montreal, Quebec, Canada, 1973)
  44. [39] R. C. Read, J. Combinatorial Theory 4, 52 (1968) O. Ore, The Four-Color Problem (Academic, New York, 1967)
  45. K. Bardakci and M. B. Halpern, Phys. Rev. D 6, 696 (1972) H. T. Grisaru, H. J. Schnitzer, and H.-S. Tsao, ibid. 8, 4498 (1973)
  46. [7] P. S. Yeung, Phys. Rev. D 13, 2306 (1976)
  47. R. Gilmore, Lie Groups, Lie Algebras and Some of Their Applications (Wiley, New York, 1974)
  48. [13,49] [50] [52], p. 25
  49. T. P. Cheng, E. Eichten, and Ling-Fong Li, Phys. Rev. D 9, 2259 (1974)
  50. D. P. Želobenko, Compact Lie Groups and Their Representations, Trans. of Math. Monographs 40 (American Math. Society, Providence, Rhode Island, 1973)
  51. Omitted endnote

  52. R. E. Behrends, J. Dreitlein, C. Fronsdal, and W. Lee, Rev. Mod. Phys. 34, 1 (1962)
  53. Macfarlane et al. ([27]) Cheng et al. ([49])
  54. M. Hamermesh, Group Theory (Addison-Wesley, Reading, Mass., 1962)
  55. D. Finkelstein, J. M. Jauch, and D. Speiser, J. Math. Phys. 4, 136 (1963) M. Gourdin, Unitary Symmetries (North-Holland, Amsterdam, 1967)
  56. [18–22,42,43], M. L. Mehta, J. Math. Phys. 7, 1824 (1966) M. L. Mehta and P. K. Srivastava, ibid. 7, 1833 (1966) J. Tits, Lecture Notes in Mathematics (Springer, New York, 1967), Vol. 40 R. Carles, Acad. Sci. Paris A276, 451 (1973) J. M. Ekins and J. F. Cornwell, Rep. Math. Phys. 7, 167 (1975) [52,58] G. Racah, Phys. Rev. 76, 1352 (1949) R. E. Behrends and A. Sirlin, ibid. 121, 324 (1961) J. Patera, J. Math. Phys. 11, 3027 (1970) J. Patera and A. K. Bose, ibid. 11, 2231 (1970) D. T. Sviridov, Yu. F. Smirnov, and V. N. Tolstoy, Rep. Math. Phys. 7, 349 (1975) R. Casalbuoni, G. Domokos, and S. Kövesi-Domokos, Nuovo Cimento 31A, 423 (1976) T. Yoshimura (unpublished)
  57. É. Cartan, Oeuvres Completes (Gauthier-Villars, Paris, 1952)
  58. M. Günaydin and F. Gürsey, J. Math. Phys. 14, 1651 (1973)
  59. R. E. Behrends et al. (Sec. V D of [52])
  60. A. Springer, Ned. Akad. Wetensch. Proc. A65, 259 (1962)
  61. H. Freudenthal, Ned. Akad. Wetensch. Proc. A57, 218 (1954)
  62. F. Gürsey, P. Ramond, and P. Sikivie, Phys. Lett. 60B, 177 (1976)
  63. J. Patera, J. Math. Phys. 12, 384 (1971)
  64. R. B. Brown, J. Reine Angew. Math. 236, 79 (1969) J. R. Faulkner, Trans. Amer. Math. Soc. 155, 397 (1971)
  65. F. Gürsey and P. Sikivie, Phys. Rev. Lett. 36, 775 (1976) Report No. 68-540 (unpublished)
  66. Omitted endnote

  67. N. J. A. Sloane, A Handbook of Integer Sequences (Academic, New York, 1973)
  68. Montmort, Essai d' Analyse sur les Jeux de Hasard (Paris, 1708) F. N. David and D. E. Barton, Combinatorial Chance (Griffin, London, 1962) Louis Comtet, Analyse Combinatoire (Presses Universitaires de France, Paris, 1970)
  69. P. Lancaster, Theory of Matrices (Academic, New York, 1969)
  70. Penrose ([39])
  71. V. K. Agrawala and J. G. Belinfante, BIT 11, 1 (1971)
  72. E. S. Abers and B. W. Lee, Phys. Rep. 9C, 1 (1973)
  73. P. Cvitanović and T. Kinoshita, Phys. Rev. D 10, 3978 (1974)
  74. Catalan, J. M. Pure Appl. 3, 508 (1838)
  75. A. C. Hearn, reduce 2, Stanford University Artificial Intelligence Project Memo AIM-133, 1970 (unpublished)

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