Discrete Kaluza-Klein from scalar fluctuations in noncommutative geometry

Journal of Mathematical Physics

Volumn 43, Issue 1, 2002, Pages 182-204

  Martinetti, Pierre ^a   Wulkenhaar, Raimar ^b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981956     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1418012     Document Type: Article

References (33)

1. A. Connes, "Gravity coupled with matter and the foundation of noncommutative geometry," Commun. Math. Phys. 182, 155-176 (1996); hep-th/9603053.
2. B. Iochum, T. Krajewski, and P. Martinetti, "Distance in finite spaces from non commutative geometry," J. Geom. Phys. 37, 100-125 (2001); hep-th/9912217.
3. R. Wulkenhaar, "Gyros as geometry of the standard model," hep-th/9712183.
4. A. Connes, Noncommutative Geometry (Academic, New York, 1994).
5. A. Connes, Géométrie Non Commutative (InterEditions, Paris, 1990).
6. A. Connes and J. Lott, "The metric aspect of noncommutative geometry," Proceedings of 1991 Cargèse Summer Conference, edited by J. FröShlich et al. (Plenum, New York, 1992).
7. A.H. Chamseddine, J. Fröhlich, and O. Grandjean, "The gravitational sector in the Connes-Lott formulations of the standard model," J. Math. Phys. 36, 6255-6275 (1995); hep-th/9503093.
8. M.A. Rieffel, "Gromov-Hanssdorff distance for quantum metric spaces," math. OA/0011063.
9. E. Atzmon, "Distances on a one-dimensional lattice from noncommutative geometry," Lett. Math. Phys. 37, 341-348 (1997); hep-th/9507002.
10. G. Bimonte, F. Lizzi, and G. Sparano, "Distances on a lattice from noncommutative geometry," Phys. Lett. B 341, 139-146 (1994); hep-lat/9404007.
11. A. Dimakis, F. Müller-Hoissen, and T. Striker, "Non-commutative differential calculus and lattice jange theory," J. Phys. A 26, 1927-1949 (1993).
12. M. Requardt, "Spectral analysis and operator theory on (infinite) graphs, graph-Laplacians and Dirac operators and the Connes-distance-functional," math-ph/0001026.
13. J. Madore and J. Mourad, "On the origine of Kaluza-Klein structure," Phys. Lett. B 359, 43 (1995); hep-th/9506041; "Noncommutative Kaluza-Klein theory," hep-th/9601169.
14. J. Madore and J. Mourad, "On the origine of Kaluza-Klein structure," Phys. Lett. B 359, 43 (1995); hep-th/9506041; "Noncommutative Kaluza-Klein theory," hep-th/9601169.
15. R. Coquereaux and A. Jadczyk, Riemannian Geometry Fibre Bundles Kaluza-Klein theories and all that..., World Scientific Lecture Notes in Physics Vol. 16 (World Scientific, Singapore, 1988).
16. J. Madore, An Introduction to Noncommutative Differential Geometry and its Physical Applications (Cambridge University Press, Cambridge, 1995).
17. A.H. Chamseddine, G. Felder, and J. Fröhlich, "Gravity in non-commutative geometry," Commun. Math. Phys. 155, 205-218 (1993); hep-th/9209044.
18. J.M. Gracia-Bondia, J.C. Varilly, and H. Figueroa, Elements of Noncommutative Geometry (Birkhauser, Boston, 2001).
19. J. Dai and X.C. Song, "Pythagoras' theorem on a 2D-lattice from a 'natural' Dirac operator and Connes' distance formula," hep-th/0101092.
20. T. Krajewski, "Noncommutative geometry and fundamental interactions," Ph.D. thesis, 1998, hep-th/9903047.
21. M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics (IOP, Bristol, 1990).
22. T. Krajewski, "Classification of finite spectral triple," J. Geom. Phys. 28, 1-30 (1997); hep-th/9701081.
23. G.J. Murphy, C*-Algebras and Operator Theory (Academic, New York, 1990).
24. R.V. Kadison, Fundamentals of the Theory of Operator Algebras (Academic, New York, 1983).
25. M. Takesaki, Theory of Operator Algebras 1 (Springer, Berlin, 1979).
26. D. Kastler and D. Testard, "Quantum forms of tensor products," Commun. Math. Phys. 155, 135-142 (1993).
27. T. Schücker and J.M. Zylinski, "Connes' model building kit," J. Geom. Phys. 16, 207-236 (1995); hep-th/9312186.
28. C. Rovelli, "Spectral noncommutative geometry and quantization: A simple example," Phys. Rev. Lett. 83, 1079-1083 (1999); gr-qc/9903045.
29. A.H. Chamseddine and A. Connes, "The spectral action principle," Commun. Math. Phys. 186, 737-750 (1996); hep-th/9606001.
30. L. Carminati, B. Iochum, and T. Schücker, "Noncommutative Yang-Mills and Noncommutative Relativity: A bridge over troubled water," Eur. Phys. J. C 8, 697-709 (1999); hep-th/9706105.
31. A.H. Chamseddine and J. Fröhlich, "Constraints on the Higgs and top quark masses from effective potential and non-commutative geometry," Phys. Lett. B 314, 308-314 (1993); hep-th/9307209.
32. B. Iochnm, D. Kastler, and T. Schücker, "On the universal Chamseddine-Connes action. I. Details of the action computation," J. Math. Phys. 38, 4929-4950 (1997); hep-th/9607158.
33. K.R. Goodearl, Notes on Real and Complex C*-algebras (Shiva, Nantwich, England, 1982.