The Hopf algebra of feynman graphs in quantum electrodynamics

Letters in Mathematical Physics

Volumn 77, Issue 3, 2006, Pages 265-281

  Van Suijlekom, Walter D ^a  

^a MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

Hopf algebras; Pertubative methods of renormalization; Quantum electrodynamics

Indexed keywords

EID: 33748057519     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-006-0092-4     Document Type: Article

References (18)

1. Broadhurst, D.J., Kreimer, D.: Renormalization automated by Hopf algebra. J. Symbolic Comput. 27, 581-600 (1999)
2. Brouder, C., Frabetti, A.: Renormalization of QED with planar binary trees. Eur. Phys. J. C19, 715-741 (2001)
3. Brouder, C., Frabetti, A.: QED Hopf algebras on planar binary trees. J. Algebra 267, 298-322 (2003)
4. Collins, J.: Renormalization. Cambridge University Press, Cambridge (1984)
5. 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. Comm. Math. Phys. 210, 249-273 (2000)
6. 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, 215-241 (2001)
7. Connes, A., Marcolli, M.: From physics to number theory via noncommutative geometry, part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory, hep-th/0411114
8. Connes, A., Marcolli, M.: Renormalization and motivic Galois theory. Int. Math. Res. Not. 76, 4073-4091 (2004)
9. Connes, A., Marcolli, M.: Quantum fields and motives. J. Geom. Phys. 56, 55-85 (2006)
10. Dyson, F.J.: The S matrix in quantum electrodynamics. Phys. Rev. 75, 1736-1755 (1949)
11. 't Hooft, G., Veltman, M.J.G.: Diagrammar. CERN Yellow Report. 73, 1-114 (1973)
12. Kreimer, D.: On the Hopf algebra structure of perturbative quantum field theories. Adv. Theor. Math. Phys. 2, 303-334 (1998)
13. Kreimer, D.: Anatomy of a gauge theory. Ann. Phys. (available online 9 March 2006)
14. Kreimer, D., Delbourgo, R.: Using the Hopf algebra structure of QFT in calculations. Phys. Rev. D 60(105025), 14 (1999)
15. Kreimer, D., Yeats, K.: An Étude in non-linear Dyson-Schwinger Equations, hep-th/0605096
16. Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Addison-Wesley, New York (1995)
17. Volovich, I.V., Prokhorenko, D.V.: Renormalizations in quantum electrodynamics, and Hopf algebras. Tr. Mat. Inst. Steklova 245, 288-295 (2004)
18. Ward, J.C.: An identity in quantum electrodynamics. Phys. Rev. 78, 182 (1950)