Noncommutative geometry and physics

AIP Conference Proceedings

Volumn 861, Issue , 2006, Pages 47-69

  Connes, Alain ^a,b  

^a PSL Research University   (France)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955694106     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.2399567     Document Type: Conference Paper

References (34)

1. H. Araki. Expumioiuil in Banach algebras. Ann. Sci. École Norm. Sup. (4) 6 (1973). 67-84.
2. J. Bacz. Fundamental Physics: where we stand today. Talk given in Luminy in February 2006 http://math.ucr.edu/home/baez/where-we-stand/where-we-stand.pdf
3. J.S. Bell, R. Jackiw,.A PCACpuzzle, Nuovo Cimento, V0I.60A (1969) 47-60.
4. P. Carticr, A mad day's work: from Grothendieck to Connes and Kontsevich. The evolution of concepts of space and symmetry. Bull. Amcr. Math. Soc. (N.S.) 38 (2001), no. 4, 389-408.
5. A. Chamseddine. A. Connes, Universal Formula for Noncommutative Geometry Actions: Unification of Gravity and the Standard Model, Phys. Rev. Lett. 77,486804871 (1996).
6. A. Chamseddine. A. Connes, The Spectral Action Principle, Comm. Math. Phys. 186, 731-750 (1997).
7. A. Chamseddine, A. Connes, Scale Invariance in the Spectral Action, hcp-th/0512169 to appear in Jour. Math. Phys
8. A. Chamseddine. A. Connes. Inner fluctuations of the spectral action, hep-th/0605011.
9. J. Collins. Renormalizalion, Cambridge Monographs in Math. Physics, Cambridge University Press, 1984.
10. A. Connes, Noncommutative geomeliy. Academic Press (1994).
11. A. Connes, Geometryfrom the spectral point of view. Lett. Math. Phys. 34 (1995), no. 3, 203-238.
12. A. Connes, Gravity coupled with matter and the foundation of noncommutative geomeliy. Comm. Math. Phys. (1995)
13. A. Connes, M. Dubois-Violette, Noncommutativefinite-dimensional manifolds. I. Spherical manifolds and related examples. Comm. Math. Phys. 230 (2002), no. 3, 539-579.
14. A. Conncs, M. Dubois-Violcttc, Moduli space and structure of noncommutative 3-spheres. Lett. Math. Phys. 66 (2003), no. 1-2,91-121.
15. A. Connes, M. Dubois-Violette, Non commutative finite-dimensional manifolds II. Moduli space and structure of noncommutative 3-spheres. ArXiv math.QA/0511337.
16. A. Conncs. D. Krcimcr. Renormalization in quantum field theory and the Riemann-Ililhert problem. I. The Hopf algebra structure of graphs and the main theorem. Comm. Math. Phys. 210 (2000), no, 1, 249-273.
17. A. Connes, D. Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem. II. The β-function, dijfeomorphisms and the renormalization group. Comm. Math. Phys. 216 (2001), no. 1, 215-241.
18. A. Conncs and G. Landi, Noncommutative manifolds, the instanion algebra and isospeclral deformations. Comm. Math. Phys. 221 (2001), no. 1, 141-159. (Pubitemid 33589830)
19. A. Connes. M. Marcolli, From Physics to Number theory via Noncommutative Geometry, II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory, to appear in "Frontiers in Number Theory. Physics, and Geometry" Vol.11. Preprint hcp-th/0411114.
20. A. Conncs, M. Marcolli, Renormalization and motivic Galois theory. International Math. Research Notices, (2004), no. 76, 4073-4091.
21. A. Connes, M. Marcolli, Dimensional regularization, anomalies, and noncommutative geometry, in preparation.
22. A. Conncs. M. Marcolli, book in preparation
23. A. Conncs. H. Moscovici. The local index formula in noncommutative geometry, GAFA, Vol. 5 (1995). 174-243.
24. P. Dclignc, Equations differentielles à points singuliers réguliers. Lecture Notes in Mathematics 163, Springer 1970.
25. H. Figueroa, J.M. Gracia-Bondía. J. Varilly, Elements of Noncommutative Geometry, Birkhäuser, 2000.
26. I. M. Gclfand, N. J. Vilcnkin, Generalized Functions Vol IV, Academic press. New-York, London, San-Dicgo(1964)
27. S. Giddings, D. Marolf. J. Hartlc, Observables in effective gravity, hcp-th/0512200.
28. G. Green, Researches on the Vibrations of Pendulums in Fluid Media, Royal Society of Edinburgh Transactions (1836) p 315-324.
29. J. Hartle, S. Hawking, Wave function of the universe. Phys. Rev. D 28, 2960 (1983)
30. D. Kastlcr, The Dirac operator and gravitation, Commun. Math. Phys. 166 (1995), 633-643.
31. D. Kastlcr, Noncommutative geometry and fundamental physical interactions: The Lagrangian level. Journal. Math. Phys. 41 (2000), 3867-3891.
32. J. Martinet, J.P. Ramis, Elementary acceleration and multisummahility, I, Ann. Inst. Henri Poincaré. Vol.54 (1991) 331-401.
33. J-P. Ramis, Series divergentes et theories asymptotiques. Bull. Soc. Math. France, 121(Panoramas ct Syntheses, suppl.) 74, 1993.
34. G. Segal. G. Wilson, Loop Groups and equations of KD Vtype Publ.math. de I'lHES, 61 (1985) 5-65.