Renormalization and motivic galois theory

International Mathematics Research Notices

Volumn , Issue 76, 2004, Pages 4073-4091

  Connes, Alain ^a,b   Marcolli, Matilde ^c  

^a l'alimentation et l'Environnement   (France)

^b VANDERBILT UNIVERSITY   (United States)

^c MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13244268440     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792804143122     Document Type: Article

References (21)

1. H. Araki, Expansional in Banach algebras, Ann. Sci. École Norm. Sup. (4) 6 (1973), 67-84.
2. D. J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory, preprint, 1996, http://arXiv.org/abs/hep-th/9604128/.
3. D. J. Broadhurst and D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, Phys. Lett. B 393 (1997), no. 3-4, 403-412.
4. P. Cartier, A mad day's work: from Grothendieck to Cannes and Kontsevich. The evolution of concepts of space and symmetry, Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 4, 389-408.
5. J. C. Collins, Renormalization. An Introduction to Renormalization, the Renormalization Group, and the Operator-Product Expansion, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984.
6. A. Connes, Symétries Galoisiennes et renormalisation, Poincaré Seminar 2002: Vacuum Energy-Renormalization, Progress in Mathematical Physics, vol. 30, Birkhäuser, Basel, 2003 241-264.
7. A. Connes and M. Karoubi, Caractère multiplicatif d'un module de Fredholm [Multiplicative character of a Fredholm module], K-Theory 2 (1988), no. 3, 431-463 (French).
8. A. Connes and D. Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem, J. High Energy Phys. 1999 (1999), no. 9, pp. 1-8.
9. _, Renormalization in quantum field theory and the Riemann-Hilbert problem. I. The Hopf algebra structure of graphs and the main theorem, Comm. Math. Phys. 210 (2000), no. 1, 249-273.
10. _, Renormalization in quantum field theory and the Riemann-Hilbert problem, II. The β-function, diffeomorphisms and the renormalization group, Comm. Math. Phys. 216 (2001), no. 1, 215-241.
11. A. Connes and M. Marcolli, From physics to number theory via noncommutative geometry. Part III, in preparation.
12. A. Connes and H. Moscovici, The local index formula in noncommutative geometry, Geom. Funct. Anal. 5 (1995), no. 2, 174-243.
13. P. Deligne and A. B. Goncharov, Groupes fondamentaux motiviques de Tate mixte, preprint, 2003, http://arXiv.org/abs/math.NT/0302267/.
14. A. B. Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry, to appear in Duke Math. J.
15. _, Multiple polylogarithms and mixed Tate motives, preprint, 2001, http://arXiv.org/abs/math.AG/0103059/.
16. M. Kontsevich, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999), no. 1, 35-72.
17. D. Kreimer, On the Hopf algebra structure of perturbative quantum field theories, Adv. Theor. Math. Phys. 2 (1998), no. 2, 303-334.
18. _, The residues of quantum field theory - numbers we should know, preprint, 2004, http://arXiv.org/abs/hep-th/0404090/.
19. J. Martinet and J.-P. Ramis, Elementary acceleration and multisummability. I, Ann. Inst. H. Poincaré Phys. Théor. 54 (1991), no. 4, 331-401.
20. M. van der Put, Differential Galois theory, universal rings and universal groups, Differential Algebra and Related Topics (Newark, NJ, 2000), World Scientific Publishing, New Jersey, 2002, pp. 171-189.
21. M. van der Put and M. F. Singer, Galois theory of linear differential equations, Grundlehren der mathematischen Wissenschaften, vol. 328, Springer, Berlin, 2003.