Feynman motives of banana graphs

Communications in Number Theory and Physics

Volumn 3, Issue 1, 2009, Pages 1-57

  Aluffi, Paolo ^a   Marcolli, Matilde ^b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 75349092555     PISSN: 19314523     EISSN: 19314531     Source Type: Journal    
DOI: 10.4310/CNTP.2009.v3.n1.a1     Document Type: Article

References (36)

1. P. Aluffi, Classes de Chern des variétés singulières, revisitées,C.R. Math. Acad. Sci. Paris 342(6) (2006), 405-410.
2. P. Aluffi, Limits of Chow groups, and a new construction of Chern- Schwartz-MacPherson classes, Pure Appl. Math. Q. 2(4) (2006), 915-941.
3. P. Aluffi, Modification systems and integration in their Chow groups, Selecta Math. (N.S.) 11(2) (2005), 155-202.
4. P. Aluffi, Computing characteristic classes of projective schemes.J. Symbolic Comput. 35(1) (2003), 3-19.
5. P. Aluffi, Chern classes for singular hypersurfaces, Trans. Amer. Math. Soc. 351(10) (1999), 3989-4026.
6. P. Aluffi, MacPherson's and Fulton's Chern classes of hypersurfaces, Internat. Math. Res. Notices, 11 (1994), 455-465.
7. P. Aluffi, M. Marcolli, Algebro-geometric Feynman rules, preprint arXiv:0811.2514.
8. P. Aluffi and L.C. Mihalcea, Chern classes of Schubert cells and vari- eties, arXiv:math/0607752, to appear in J. Algebraic Geom.
9. P. Belkale, P. Brosnan, Matroids, motives, and a conjecture of Kontse- vich, Duke Math. J. 116 (2003), 147-188.
10. P. Belkale and P. Brosnan, Periods and Igusa local zeta functions,Int. Math. Res. Not. (49) (2003), 2655-2670.
11. J. Bjorken and S. Drell, Relativistic quantum mechanics, McGraw-Hill, New York, 1964, and Relativistic quantum fields, McGraw-Hill, New York, 1965.
12. S. Bloch, Motives associated to graphs, Japan J. Math. 2 (2007), 165-196.
13. S. Bloch, Motives associated to sums of graphs, arXiv:0810.1313.
14. S. Bloch, E. Esnault and D. Kreimer, On motives associated to graph polynomials, Commun. Math. Phys. 267 (2006), 181-225.
15. S. Bloch and D. Kreimer, Mixed Hodge structures and renormalization in physics, arXiv:0804.4399.
16. C. Bogner and S. Weinzierl, Periods and Feynman integrals, arXiv:0711.4863.
17. J.-P. Brasselet, D. Lehmann, J. Seade and T. Suwa, Milnor classes of local complete intersections, Trans. Amer. Math. Soc. 354(4) (2002), 1351-1371.
18. J.P. Brasselet and M.H. Schwartz, Sur les classes de Chern d'un ensemble analytique complexe, in 'The Euler-Poincaré characteristic', Astérisque, Vol. 83, Soc. Math., France, 1981, 93-147.
19. D. Broadhurst and D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, Phys. Lett. B 393 (1997), 403-412.
20. A. Connes, M. Douglas and A. Schwarz, Noncommutative geometry and matrix theory: compactification on tori, JHEP 9802 (1998), 3-43.
21. A. Connes and D. Kreimer, Renormalization in quantum field the- ory and the Riemann-Hilbert problem I. The Hopf algebra structure of graphs and the main theorem, Comm. Math. Phys. 210 (2000), 249-273.
22. W. Fulton, Intersection theory. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 2, Springer-Verlag, 1984, xi+470 pp.
23. H. Gillet and C.Soulé, Descent, motives and K-theory, J. Reine Angew. Math. 478 (1996), 127-176.
24. D.R. Grayson and M.E. Stillman, Macaulay 2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/
25. H. Grosse and R. Wulkenhaar, Renormalization of noncommutative quantum field theory, in 'An invitation to Noncommutative Geometry', eds. M. Khalkhali and M. Marcolli, World Scientific, Singapore, 2008, 129-168.
26. R. Gurau and V. Rivasseau, Parametric representation of noncommu- tative field theory, Commun. Math. Phys. 272(3) (2007), 811-835.
27. C. Itzykson and J.B. Zuber, Quantum field theory, Dover Publications, New York, 2006.
28. M. Kwieciński, Formule du produit pour les classes caractéristiques de Chern-Schwartz-MacPherson et homologie d'intersection, C. R. Acad. Sci. Paris Sér. I Math., 314(8) (1992), 625-628.
29. R.D. MacPherson, Chern classes for singular algebraic varieties, Ann. Math. 100(2) (1974), 423-432.
30. M. Marcolli, Motivic renormalization and singularities, arXiv: 0804.4824.
31. N. Nakanishi, Graph theory and Feynman integrals. Gordon and Breach, London, 1971.
32. A. Parusiński, A generalization of the Milnor number, Math. Ann. 281(2) (1988), 247-254.
33. M.H. Schwartz, Classes caractéristiques définies par une stratification d'une variété analytique complexe. I, C. R. Acad. Sci. Paris 260 (1965), 3262-3264.
34. M.H. Schwartz, Classes caractéristiques définies par une stratification d'une variété analytique complexe, C. R. Acad. Sci. Paris, 260 (1965), 3535-3537.
35. N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 9909 (1999), 32-131.
36. A. Tanasa, Overview of the parametric representation of renormalizable non-commutative field theory, arXiv:0709.2270.