Combinatorics of (perturbative) quantum field theory
High Energy Physics - Theory
2009-10-31 v1 High Energy Physics - Phenomenology
Mathematical Physics
math.MP
Quantum Algebra
Abstract
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.
Cite
@article{arxiv.hep-th/0010059,
title = {Combinatorics of (perturbative) quantum field theory},
author = {Dirk Kreimer},
journal= {arXiv preprint arXiv:hep-th/0010059},
year = {2009}
}
Comments
47p, to appear in a special volume of Phys. Reports dedicated to the Renormalization Group