Factorization in quantum field theory: An exercise in hopf algebras and local singularities

Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization

Volumn , Issue , 2007, Pages 715-736

  Kreimer, Dirk ^a  

^a INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

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EID: 77954390791     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-30308-4_14     Document Type: Chapter

References (35)

1. Kreimer, D.: New mathematical structures in renormalizable quantum field theories. Annals Phys. 303 (2003) 179 [Erratumibid. 305 (2003) 79] [arXiv:hep-th/0211136].
2. C. Bergbauer and D. Kreimer, Hopf Algebras in Renormalization Theory: Locality and DysonSchwinger Equations from Hochschild Cohomology, in IRMA lectures in Mathematics and Theoretical Physics Vol. 10, Physics and Number Theory, European Mathematical Society, Eds. V. Turaev, L. Nyssen.
3. Kreimer, D.: Anatomy of a gauge theory, preprint hep-th/0509135, Annals of Physics (2006), e-published, paper version in press.
4. Gangl, H, Goncharov, A.B., Levin, A.: Multiple logarithms, algebraic cycles and trees. Frontiers in Number Theory, Physics, and Geometry II, pp. 759-774.
5. Cartier, P: A primer of hopf algebras. Frontiers in Number Theory, Physics, and Geometry II, pp. 537-616.
6. Goncharov, A.: Galois symmetries of fundamental groupoids and non-commutative geometry. IHES/M/02/56, www.ihes.fr.
7. Zagier, D.: Polylogarithms. Lectures at this school.
8. Bern, Z.: Perturbative calculations in gauge and gravity theories. Talk at this school.
9. Weinzierl, S.: Algebraic algorithms in perturbative calculations. Frontiers in Number Theory, Physics, and Geometry II, pp. 737-758, [arXiv:hep-th/0305260].
10. Kreimer, D.: On the Hopf algebra structure of perturbative quantum field theories. Adv. Theor. Math. Phys. 2 (1998) 303 [arXiv:q-alg/9707029].
11. Kreimer, D.: On overlapping divergences. Commun. Math. Phys. 204 (1999) 669 [arXiv:hep-th/9810022].
12. Connes, A., Kreimer, D.: Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem. Commun. Math. Phys. 210 (2000) 249 [arXiv:hep-th/9912092].
13. Connes, A., Kreimer, D.: Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs. Annales Henri Poincare 3 (2002) 411 [arXiv:hep-th/0201157].
14. Johnson, K., R. Willey, R., and Baker, M.: Vacuum Polarization In Quantum Electrodynamics. Phys. Rev. 163 (1967) 1699.
15. Broadhurst, D.J., Delbourgo, R., Kreimer, D.: Unknotting the polarized vacuum of quenched QED. Phys. Lett. B 366 (1996) 421 [arXiv:hep-ph/9509296].
16. Kreimer, D.: Chen's iterated integral represents the operator product expansion. Adv. Theor. Math. Phys. 3 (1999) 627 [arXiv:hep-th/9901099].
17. Broadhurst, D.J., Kreimer, D.: Renormalization automated by Hopf algebra. J. Symb. Comput. 27 (1999) 581 [arXiv:hep-th/9810087].
18. Kreimer, D.: Unique factorization in perturbative QFT. Nucl. Phys. Proc. Suppl. 116 (2003) 392 [arXiv:hep-ph/0211188].
19. Foissy, L.: Les alg̀ebres des Hopf des arbres enracinés décorées. [arXiv:math. QA/0105212].
20. Connes, A., Kreimer, D.: Hopf algebras, renormalization and noncom-mutative geometry. Commun. Math. Phys. 199 (1998) 203 [arXiv:hep-th/9808042].
21. Broadhurst, D.J., Kreimer, D.: Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality. Nucl. Phys. B 600 (2001) 403 [arXiv:hep-th/0012146].
22. Rivers, R.J.: Path integrals methods in quantum field theory. CUP, Cambridge (1987).
23. Cvitanovic, P.: Field Theory. RX-1012 (NORDITA) (http://www.cns.gatech. edu/FieldTheory/).
24. Weinberg, S.: High-Energy Behavior In Quantum Field Theory. Phys. Rev. 118 (1960) 838.
25. Kreimer, D.: Knots And Feynman Diagrams. CUP, Cambridge (2000).
26. Belkale P., Brosnan, P.: Matroids, Motives and a conjecture of Kontse-vich. Duke Math. J. 116 (2002) 147 [arXiv:math.AG/0012198].
27. 3 in Finite Quantum Electrodynamics. Phys. Rev. Lett. 17 (1966) 1190.
28. Cvitanovic, P.: Asymptotic Estimates And Gauge Invariance. Nucl. Phys. B 127 (1977) 176.
29. Broadhurst, D.J., Kreimer, D.: Feynman diagrams as a weight system: Four-loop test of a four-term relation. Phys. Lett. B 426 (1998) 339 [arXiv:hep-th/9612011].
30. Broadhurst, D.J., Kreimer, D.: Towards cohomology of renormalization: Bigrading the combinatorial Hopf algebra of rooted trees. Commun. Math. Phys. 215 (2000) 217 [arXiv:hep-th/0001202].
31. Connes, A., Kreimer, D.: Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The beta-function, diffeomorphisms and the renormalization group. Commun. Math. Phys. 216 (2001) 215 [arXiv:hep-th/0003188] .
32. Kreimer, D., Delbourgo, R.: Using the Hopf algebra structure of QFT in calculations. Phys. Rev. D 60 (1999) 105025 [arXiv:hep-th/9903249].
33. Coleman, S.: Aspects of Symmetry, Lect. 3: Dilatations. Cambridge University Press, Cambridge (1985).
34. Kreimer, D.: The residues of quantum field theory: Numbers we should know, in Proc. Arithmetic and Number Theory in Noncommutative Geometry, Bonn August 2003, Consani, K., Marcolli, M., eds., Max Planck Monographs, Vieweg, to appear. arXiv:hep-th/0404090.
35. Bergbauer, C., Kreimer, D.: The Hopf algebra of rooted trees in Epstein-Glaser renormalization, Annales Henri Poincare 6 (2005) 343 [arXiv:hep-th/0403207].