Algèbre de Hopf des diagrammes de Feynman, renormalisation et factorisation de Wiener-Hopf

Louis Boutet de Monvel

Séminaire Bourbaki (2001-2002)

  • Volume: 44, page 149-165
  • ISSN: 0303-1179

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Boutet de Monvel, Louis. "Algèbre de Hopf des diagrammes de Feynman, renormalisation et factorisation de Wiener-Hopf." Séminaire Bourbaki 44 (2001-2002): 149-165. <http://eudml.org/doc/110302>.

@article{BoutetdeMonvel2001-2002,
author = {Boutet de Monvel, Louis},
journal = {Séminaire Bourbaki},
language = {fre},
pages = {149-165},
publisher = {Société Mathématique de France},
title = {Algèbre de Hopf des diagrammes de Feynman, renormalisation et factorisation de Wiener-Hopf},
url = {http://eudml.org/doc/110302},
volume = {44},
year = {2001-2002},
}

TY - JOUR
AU - Boutet de Monvel, Louis
TI - Algèbre de Hopf des diagrammes de Feynman, renormalisation et factorisation de Wiener-Hopf
JO - Séminaire Bourbaki
PY - 2001-2002
PB - Société Mathématique de France
VL - 44
SP - 149
EP - 165
LA - fre
UR - http://eudml.org/doc/110302
ER -

References

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  1. [CK1] A. Connes & D. Kreimer — « 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, p. 249-273. Zbl1032.81026MR1748177
  2. [CK2] _, « 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, p. 215-241. Zbl1042.81059
  3. [BK1] D.J. Broadhurst & D. Kreimer — « Knots and numbers in Ø4 theory to 7 loops and beyond », Internat. J. Modern Phys. C6 (1995), no. 4, p. 519-524. Zbl0940.81520MR1352337
  4. [BK2] _, « Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops », Phys. Lett. B393 (1997), no. 3-4, p. 403-412. Zbl0946.81028MR1435933
  5. [BK3] D.J. Broadhurst, J.A. Gracey & D. Kreimer — « Beyond the triangle and uniqueness relations : non-zeta counterterms at large N from positive knots », Z. Phys. C75 (1997), no. 3, p. 559-574. MR1461268
  6. [BK4] D.J. Broadhurst & D. Kreimer — « Feynman diagrams as a weight system : four-loop test of a four-term relation », Phys. Lett. B426 (1998), no. 3-4, p. 339-346. Zbl1049.81568MR1629951
  7. [BK5] _, « Renormalization automated by Hopf algebra », J. Symbolic Comput.27 (1999), no. 6, p. 581-600, and hep-th/9810087. Zbl1049.81048MR1701096
  8. [BK6] _, « Combinatoric explosion of renormalization tamed by Hopf algebra : 30-loop Padé-Borel resummation », Phys. Lett. B475 (2000), no. 1-2, p. 63- 70, and hep-th/9912093. Zbl1049.81569MR1748409
  9. [BK7] _, « Towards cohomology of renormalization : bigrading the combinatorial Hopf algebra of rooted trees », Comm. Math. Phys.215 (2000), no. 1, p. 217-236. Zbl0986.16015MR1800924
  10. [CK3] A. Connes & D. Kreimer — « Hopf algebras, renormalization and noncommutative geometry », Comm. Math. Phys.199 (1998), no. 1, p. 203-242. Zbl0932.16038MR1660199
  11. [CK4] _, « Hopf algebras, renormalization and noncommutative geometry », in Quantum field theory : perspective and prospective (Les Houches 1998), NATO Sci. Ser. C Math. Phys. Sci., vol. 530, Kluwer Acad. Publ., Dordrecht, 1999, p. 59-108. Zbl1041.81086MR1725011
  12. [CK5] _, « Renormalization in quantum field theory and the Riemann-Hilbert problem », J. High Energy Phys. (1999), no. 9, p. Paper 24, 8 pp., (electronic) and hep-th/9909126. Zbl0957.81011MR1720691
  13. [CK6] _, « Lessons from quantum field theory : Hopf algebras and spacetime geometries, Moshé Flato (1937-1998) », Lett. Math. Phys.48 (1999), no. 1, p. 85-96, and hep-th/9904044. Zbl0965.81046MR1718046
  14. [CK7] _, « From local perturbation theory to Hopfand Lie-algebras of Feynman graphs », in Mathematical physics in mathematics and physics (Siena, 2000), Fields Inst. Commun., vol. 30, Amer. Math. Soc., 2001, p. 105-114. Zbl1015.81042MR1867549
  15. [DK] R. Delbourgo & D. Kreimer — « Using the Hopf algebra structure of QFT in calculations », Phys. Rev. D (3) 60 (1999), no. 10, and hep-th/9903249. MR1757650
  16. [K1] D. Kreimer — « Renormalization and knot theory », J. Knot Theory and Ramifications6 (1997), no. 4, p. 479-581. Zbl0893.57005MR1466595
  17. [K2] _, « On the Hopf algebra structure of perturbative quantum field theories », Adv. Theor. Math. Phys.2 (1998), no. 2, p. 303-334. Zbl1041.81087MR1633004
  18. [K3] _, « On overlapping divergences », Comm. Math. Phys.204 (1999), no. 3, p. 669-689, and hep-th/9810022. Zbl0977.81091MR1707611
  19. [K4] _, « Chen's iterated integral represents the operator product expansion », Adv. Theor. Math. Phys.3 (1999), no. 3, and hep-th/9901099. Zbl0971.81093
  20. [K5] _, Knots and Feynman diagrams, Cambridge Lecture Notes in Physics, vol. 13, Cambridge University Press, Cambridge, 2000. Zbl0964.81052MR1778151
  21. [K6] _, « Shuffling quantum field theory », Lett. Math. Phys.51 (2000), no. 3, p. 179-191. Zbl1053.81071MR1775420
  22. [Coll] J. Collins — Renormalization,, Cambridge monographs in math. phys., Cambridge University Press, Cambridge, 1984. Zbl1094.53505MR778558
  23. [Dres] M. Dresden — « Renormalization in historical perspective - The first stage », in Renormalization, Springer-Verlag, New York, Berlin, Heidelberg, 1994. MR1258529
  24. [Drou] J.-M. Drouffe & C. Itzykson — Théorie statistique des champs, Savoirs actuels, InterEditions/Editions du C.N.R.S., 1989, 2 volumes. 
  25. [EG] H. Epstein & V. Glaser — « The role of locality in perturbation theory », Ann. Inst. H. Poincaré A19 (1973), p. 211-295. Zbl1216.81075MR342091
  26. [FMRS] J. Feldman, J. Magnen, V. Rivasseau & R. Seneor — « Massive Gross-Neveu model : a rigorous perturbative construction », Phys. Rev. Lett.54 (1985). MR787776
  27. [GK] K. Gawedski & A. Kupianen — « Exact renormalization of the Gross-Neveu model of quantum fields », Phys. Rev. Lett54 (1985). 
  28. [GJ] J. Glimm & A. Jaffe — Quantum Physics, Springer-Verlag, New York, Berlin, Heidelberg, 1987. Zbl0461.46051MR887102
  29. [LeBe] M. Le Bellac — Des phénomènes critiques aux champs de jauge, Savoirs actuels, InterEditions/Editions du C.N.R.S., 1988. MR937513
  30. [ZJ] J. Zinn-Justin — Quantum Field Theory and Critical Phenomena, International series of monographies on physics, vol. 92, Oxford science publications, 1996. Zbl0865.00014MR1079938
  31. [Beau] A. Beauville — « Monodromie des systèmes différentiels linéaires à pôles simples sur la sphère de Riemann », in Sém. Bourbaki, Astérisque, vol. 216, Soc. Math. France, Paris, 1993, exp. n° 765 (mars 1993), p. 103-119. Zbl0796.34007MR1246395
  32. [Boli] A. Bolibruch — « Fuchsian systems with reducible monodromy and the Riemann-Hilbert problem », Lecture Notes in Math., vol. 1250, Springer, 1992, p. 139-155. Zbl0796.30038MR1178278
  33. [BKI] N. Bourbaki — Éléments de mathématique. Algèbre. Chapitres 1 à 3, Masson, Paris, 1982. MR643362
  34. [ENS] L. Boutet De Monvel, A. Douady & J.-L. Verdier (éds.) - Mathématique et Physique, Séminaire de l'E.N.S. 1979-82, Progress in Math., vol. 35, Birkhäuser, 1983. Zbl0516.00021MR728411
  35. [Drin] V.G. Drinfel'd — « Almost cocommutative Hopf algebras », Algebra i Analiz1 (1989), no. 2, p. 30-46, and translation in Leningrad Math. J.1 (1990), no. 2, p. 321-342. Zbl0718.16035MR1025154
  36. [WH] I. Gohberg & M.A. Kaashoek (éds.) - Constructive methods of Wiener-Hopf factorization, Operator Theory : Advances and Applications, vol. 21, Birkhäuser Verlag, Basel, 1986. Zbl0612.47025MR902611
  37. [LP] I. Lappo-Danilevskii — Mémoire sur la théorie des systèmes d'équations différentielles linéaires, Chelsea, New York, 1953. Zbl0051.32301
  38. [Pat1] F. Patras & C. Reutenauer — « Higher Lie idempotents », J. Algebra222 (1999), no. 1, p. 51-64. Zbl0956.16017MR1728169
  39. [Pat2] F. Patras — « La décomposition en poids des algèbres de Hopf », Ann. Inst. Fourier43 (1993), no. 4, p. 1067-1087. Zbl0795.16028MR1252938
  40. [Spe] F.-O. Speck — General Wiener-Hopf factorization methods, vol. 119, Pitman (Advanced Publishing Program), Boston, MA, 1985, With a foreword by E. Meister. Zbl0588.35090MR790315
  41. [BCE] J. Brodzki, A. Connes & D. Ellwood — « Polarized modules and Fredholm modules », Mat. Fiz. Anal. Geom.2 (1995), no. 1, p. 15-24. Zbl0842.46031MR1484114
  42. [C1] A. Connes - Noncommutative geometry, Academic Press, Inc., San Diego, CA, 1994, 661 pp. Zbl0818.46076MR1303779
  43. [C2] _, « Non-commutative geometry and physics », in Gravitation et quantifications (Les Houches, 1992), North-Holland, Amsterdam, 1995, p. 805- 950. Zbl0933.46069MR1461287
  44. [C3] _, « Géométrie non commutative et physique quantique », in Mathématiques quantiques, SMF Journ. Annu., Soc. Math. France, Paris, 1992, 20 pp. Zbl0942.58015MR1484740
  45. [C4] _, « The action functional in noncommutative geometry », Comm. Math. Phys.117 (1988), no. 4, p. 673-683. Zbl0658.53068MR953826
  46. [CM] A. Connes & H. Moscovici — « Hopf algebras, cyclic cohomology and the transverse index theorem », Comm. Math. Phys.198 (1998), no. 1, p. 199- 246. Zbl0940.58005MR1657389
  47. [CS] A. Connes & E. Størmer — « A connection between the classical and the quantum mechanical entropies », in Operator algebras and group representations (Neptun, 1980), vol. I, Monographs Stud. Math., vol. 17, Pitman, Boston, Mass.-London, 1984, p. 113-123. Zbl0543.46040MR731767

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