The standard model as a noncommutative geometry: The low-energy regime

Physics Report

Volumn 294, Issue 6, 1998, Pages 363-406

  Martin C P ^a   Gracia Bondía, José M ^b   Várilly, Joseph C ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSIDAD DE COSTA RICA   (Costa Rica)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031989814     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(97)00053-7     Document Type: Review

References (65)

1. [1] A. Connes, in: D.G. Quillen, G.B. Segal, S.T. Tsou (Eds.), The Interface of Mathematics and Particle Physics, Clarendon Press, Oxford, 1990.
2. [2] A. Connes, J. Lott, Nucl. Phys. B (Proc. Suppl.) 18 (1990) 29.
3. [3] A. Connes, Noncommutative Geometry, Academic Press, London, 1994.
4. [4] M.J. Herrero, preprint hep-ph/9601286, Madrid, 1996.
5. [5] A. Connes, Commun. Math. Phys. 182 (1996) 155.
6. [6] J.C. Várilly, J.M. Gracia-Bondía, J. Geom. Phys. 12 (1993) 223.
7. [7] F. Abe et al. (CDF collaboration), Phys. Rev. Lett. 74 (1995) 2626.
8. [8] S. Abachi et al. (D0 collaboration), Phys. Rev. Lett. 74 (1995) 2632.
9. [9] E. Alvarez, J.M. Gracia-Bondía, C.P. Martín, Phys. Lett. B 306 (1993) 55.
10. [10] E. Alvarez, J.M. Gracia-Bondía, C.P. Martín, Phys. Lett. B 329 (1994) 259.
11. [11] A. Connes, Conf. Noncommutative Geometry and Its Applications, Třešť, Czech Republic, May 1995.
12. [12] A. Connes, J. Math. Phys. 36 (1995) 6194.
13. [13] J.M. Gracia-Bondía, Phys. Lett. B 351 (1995) 510.
14. [14] D. Kastler, T. Schücker, Rev. Math. Phys. 8 (1996) 205.
15. [15] T. Schücker, J.-M. Zylinski, J. Geom. Phys. 16 (1995) 207.
16. [16] B. Iochum, T. Schücker, Commun. Math. Phys. 178 (1996) 1.
17. [17] F. Lizzi, G. Mangano, G. Miele, G. Sparano, Mod. Phys. Lett. A 11 (1996) 2561.
18. [18] D. Testard, unpublished manuscript, 1995.
19. [19] E. Alvarez, J.M. Gracia-Bondía, C.P. Martín, Phys. Lett. B 364 (1995) 33.
20. [20] P.A.M. Dirac, The Principles of Quantum Mechanics, 4th ed., Clarendon Press, Oxford, 1958.
21. [21] T.-P. Cheng, L.-F. Li, Gauge Theory of Elementary Particle Physics, Clarendon Press, Oxford, 1988.
22. [22] J.F. Donoghue, E. Golowich, B.R. Holstein, Dynamics of the Standard Model, Cambridge University Press, Cambridge, 1992.
23. [23] M. Nakahara, Geometry, Topology and Physics, Adam Hilger, Bristol, 1990.
24. [24] E. Wirten, Nucl. Phys. B 186 (1931) 412.
25. [25] T. Appelquist, A. Chodos, P.G.O. Freund, Modern Kaluza-Klein theories, Addison-Wesley, Reading, MA, 1987.
26. [26] G. Cammarata, R. Coquereaux, Lecture Notes in Physics 469, Springer, 1995, p. 27.
27. [27] M.E.. Peskin, D.V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley, Reading, MA, 1995.
28. [28] R.E. Marshak, Conceptual Foundations of Modem Particle Physics, World Scientific, Singapore, 1993.
29. [29] J.M. Gracia-Bondía, in: E.C.G. Sudarshan (Ed.), A Gift of Prophecy, Essays in Celebration of the life of Robert Eugene Marshak, World Scientific, Singapore, 1995.
30. [30] A. Connes, Commun. Math. Phys. 117 (1988) 673.
31. [31] J. Plass, Dìplomarbeit, Universität Mainz, 1993.
32. [32] W. Kalau, N.A. Papadopoulos, J. Plass, J.-M. Warzecha, J. Geom. Phys. 16 (1995) 149.
33. [33] F. Cipriani, D. Guido, S. Scarlatti, J. Operator Theory 35 (1996) 179.
34. [34] D. Kastler, Commun. Math. Phys. 166 (1995) 633.
35. [35] W. Kalau, M. Walze, J. Geom. Phys. 16 (1995) 327.
36. [36] A. Connes, private communication.
37. [37] A.H. Chamseddine, A. Connes, Commun. Math. Phys. 186 (1997) 731.
38. [38] W. Kalau, J. Geom. Phys. 18 (1996) 349.
39. [39] L. Carminati, B. Iochum, D. Kastler, T. Schücker, preprint hep-th/9612228, Luminy, 1996.
40. [40] F. Lizzi, G. Mangano, G. Miele, G, Sparano, preprint hep-th/9610035, Napoli and Oxford, 1996.
41. [41] R. Coquereaux, G. Esposito-Farèse, F. Scheck, Int. J. Mod. Phys. A 7 (1992) 6555.
42. [42] R. Häußling, F. Scheck, Phys. Lett. B 336 (1994) 477.
43. [43] L. Carminati, B. Iochum, T. Schücker, J. Math. Phys. 38 (1997) 1269.
44. [44] R.M. Barnett et al., Phys. Rev. D 54 (1996) 1.
45. [45] W.F.L. Hollick, Fortschr. Phys. 78 (1990) 165.
46. [46] S. Franchiotti, A. Sirlin, Phys. Rev. D 41 (1990) 319 and references therein.
47. [47] M.E. Machacek, M.T. Vaughn, Nucl. Phys. B 222 (1983) 83; Nucl. Phys. B 236 (1984) 221; Nucl. Phys. B 249 (1985) 70.
48. [47] M.E. Machacek, M.T. Vaughn, Nucl. Phys. B 222 (1983) 83; Nucl. Phys. B 236 (1984) 221; Nucl. Phys. B 249 (1985) 70.
49. [47] M.E. Machacek, M.T. Vaughn, Nucl. Phys. B 222 (1983) 83; Nucl. Phys. B 236 (1984) 221; Nucl. Phys. B 249 (1985) 70.
50. [48] P. Langacker (Ed.), Precision Tests of the Standard Electroweak Model, World Scientific, Singapore, 1995.
51. [49] G. Veneziano, summary talk at the 9th Int. Workshop on Supersymmetry and Unification of Fundamental Forces, Palaiseau, 13-19 May 1995, CERN-TH-95-332.
52. [50] J. Kubo, Phys. Lett. B 472 (1991) 262.
53. [51] A.H. Chamseddine, G. Felder, J. Fröhlich, Nucl. Phys. B 395 (1993) 672; A.H. Chamseddine, J. Fröhlich, Phys. Lett. B 314 (1993) 308; A.H. Chamseddine, J. Fröhlich, O. Grandjean, J. Math. Phys. 36 (1995) 6255, inter alia.
54. [51] A.H. Chamseddine, G. Felder, J. Fröhlich, Nucl. Phys. B 395 (1993) 672; A.H. Chamseddine, J. Fröhlich, Phys. Lett. B 314 (1993) 308; A.H. Chamseddine, J. Fröhlich, O. Grandjean, J. Math. Phys. 36 (1995) 6255, inter alia.
55. [51] A.H. Chamseddine, G. Felder, J. Fröhlich, Nucl. Phys. B 395 (1993) 672; A.H. Chamseddine, J. Fröhlich, Phys. Lett. B 314 (1993) 308; A.H. Chamseddine, J. Fröhlich, O. Grandjean, J. Math. Phys. 36 (1995) 6255, inter alia.
56. [52] R. Wulkenhaar, J. Math. Phys. 37 (1996) 3797.
57. [53] M. Dubois-Violette, R. Kerner, J. Madore, Phys. Lett. B 217 (1989) 485; J. Math. Phys. 31 (1990) 316, 323, inter alia.
58. [53] M. Dubois-Violette, R. Kerner, J. Madore, Phys. Lett. B 217 (1989) 485; J. Math. Phys. 31 (1990) 316, 323, inter alia.
59. [54] D. Sullivan, Lecture Notes in Maths. 197, Springer, Berlin, 1971.
60. [55] R.E. Asquith, Phys. Lett. B 366 (1996) 220.
61. [56] I. Pris, T. Schücker, preprint hep-th/9604115, Luminy, 1996.
62. [57] C. Geng, R. Marshak, Phys. Rev. D 39 (1989) 693.
63. [58] J. Minahan, P. Ramond, R.C. Warner, Phys. Rev. D 41 (1990) 715.
64. [59] L. Alvarez-Gaumé, E. Wirten, Nucl. Phys. B 234 (1983) 269.
65. [60] A.C. Clarke, Rendezvous with Rama: "the Ramans do everything in threes", Bantam, New York, 1973.