Internal space for the noncommutative geometry standard model and strings

International Journal of Modern Physics A

Volumn 22, Issue 7, 2007, Pages 1317-1334

  Lizzi, Fedele ^a,b  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b INFN SEZIONE DI NAPOLI   (Italy)

Author keywords

Connes Lott model; Noncommutative geometry; Standard model; String compactification

Indexed keywords

EID: 34047095755     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X07035318     Document Type: Article

References (38)

1. A. Connes and J. Lott, Nucl. Phys. B (Proc. Suppl.) 18, 29 (1991).
2. A. Connes, Noncommutative Geometry (Academic Press, 1994).
3. J. M. Gracia-Bondia, J. C. Varilly and H. Figueroa, Elements of Noncommutative Geometry (Birkhäuser, 2000).
4. M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory (Cambridge University Press, 1987).
5. J. Polchinski, String Theory (Cambridge University Press, 1998).
6. A. H. Chamseddine and A. Connes, Phys. Rev. Lett. 77, 4868 (1996).
7. A. H. Chamseddine and A. Connes, Commun. Math. Phys. 186, 731 (1997), hep-th/9606001.
8. J. W. Barrett, A Lorentzian version of the non-commutative geometry of the standard model of particle physics, hep-th/0608221.
9. A. Connes, Noncommutative geometry and the standard model with neutrino mixing, hep-th/0608226.
10. C. P. Martin, J. M. Gracia-Bondia and J. C. Varilly, Phys. Rep. 294, 363 (1998), hep-th/9605001.
11. T. Schücker, Geometries and forces, Talk given at European Mathematical Society Summer School on Noncommutative Geometry and Applications, Monsaraz and Lisbon, Portugal, 1-10 Sep. 1997, hep-th/9712095.
12. A. Connes, J. Math. Phys. 36, 6194 (1995).
13. A. Connes, Commun. Math. Phys. 182, 155 (1996), hep-th/9603053.
14. B. Iochum, D. Kastler and T. Schücker, J. Math. Phys. 38, 4929 (1997), hep-th/9607158.
15. N. Berline, E. Getzler and M. Vergne, Heat Kernels and Dirac Operators (Springer-Verlag, 1991).
16. P. B. Gilkey, Invariance Theory, The Heat Equation, and The Atiyah-Singer Index Theorem, 2nd edn., Studies in Advanced Mathematics (CRC Press, 1995).
17. M. Knecht and T. Schucker, Phys. Lett. B 640, 272 (2006), hep-ph/0605166.
18. J. M. Gracia-Bondia, F. Lizzi, G. Marmo and P. Vitale, J. High Energy Phys. 0204, 026 (2002), hep-th/0112092.
19. A. Strohmaier, J. Geom. Phys. 56, 175 (2006), math-ph/0110001.
20. W. D. van Suijlekom, J. Math. Phys. 45, 537 (2004), math-ph/0310009.
21. F. Lizzi, G. Mangano, G. Miele and G. Sparano, Phys. Rev. D 55, 6357 (1997), hep-th/9610035.
22. R. Schelp, Int. J. Mod. Phys. B 14, 2477 (2000), hep-th/9905047.
23. J. W. Barrett and R. A. Dawe Martins, J. Math. Phys. 47, 052305 (2006), hep-th/0601192.
24. L. Dabrowski, G. Landi, M. Paschke and A. Sitarz, The spectral geometry of the equatorial podles sphere, math.qa/0408034.
25. E. Alvarez, J. M. Gracia-Bondia and C. P. Martin, Phys. Lett. B 364, 33 (1995), hep-th/9506115.
26. B. Iochum, D. Kastler and T. Schücker, Fuzzy mass relations in the standard model, hep-th/9507150.
27. F. Lizzi, G. Mangano, G. Miele and G. Sparano, Mod. Phys. Lett. A 13, 231 (1998), hep-th/9704184.
28. J. M. Gracia-Bondia, B. Iochum and T. Schucker, Phys. Lett. B 416, 123 (1998), hep-th/9709145.
29. P. Podles, Lett. Math. Phys. 14, 193 (1987).
30. H. Figueroa, J. M. Gracia-Bondia, F. Lizzi and J. C. Varilly, J. Geom. Phys. 26, 329 (1998), hep-th/9701179.
31. D. Quillen, Topology 24, 89 (1985).
32. N. Seiberg and E. Witten, J. High Energy Phys. 9909, 032 (1999), hep-th/9908142.
33. J. Frohlich and K. Gawedzki, Conformal field theory and geometry of strings, hep-th/9310187.
34. J. Frohlich, O. Grandjean and A. Recknagel, Supersymmetric quantum theory, non-commutative geometry, and gravitation, hep-th/9706132.
35. F. Lizzi and R. J. Szabo, Phys. Rev. Lett. 79, 3581 (1997), hep-th/9706107.
36. F. Lizzi and R. J. Szabo, Commun. Math. Phys. 197, 667 (1998), hep-th/9707202.
37. G. Landi, F. Lizzi and R. J. Szabo, Commun. Math. Phys. 206, 603 (1999), hep-th/9806099.
38. I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B 436, 257 (1998), hep-ph/9804398.