Renormalization in Quantum Electrodynamics and Hopf Algebras

Recently, A. Connes and D. Kreimer introduced the Hopf algebra structure on Feynman graphs in scalar quantum field theory and show that the renormalization can be reduced to the solution of the Riemann–Hilbert problem. In this paper, we suggest a generalization of their construction to the case of quantum electrodynamics. Moreover, we define the action of a gauge group on the Hopf algebra of Feynman diagrams and clarify how this action interacts with the Hopf algebra structure.

Received in February 2004