Combinatorics of (perturbative) quantum field theory

Details Combinatorics of (perturbative) quantum field theory Combinatorics of (perturbative) quantum field theory

2000-10-09

arxiv.org/abs/hep-th/0010059v1

Phys.Rept. 363 (2002) 387-424

Physics

High Energy Physics

High Energy Physics - Theory

47p, to appear in a special volume of Phys. Reports dedicated to the Renormalization Group

Scientific paper

10.1016/S0370-1573(01)00099-0

We review the structures imposed on perturbative QFT by the fact that its Feynman diagrams provide Hopf and Lie algebras. We emphasize the role which the Hopf algebra plays in renormalization by providing the forest formulas. We exhibit how the associated Lie algebra originates from an operadic operation of graph insertions. Particular emphasis is given to the connection with the Riemann--Hilbert problem. Finally, we outline how these structures relate to the numbers which we see in Feynman diagrams.

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