We discuss the Hopf algebraic description of renormalization theory of quantum electrodynamics. The Ward identities are implemented as linear relations on the Hopf algebra of Feynman graphs of QED. Compatibility of these relations with the Hopf algebra structure is the mathematical formulation of the physical fact that Ward identities are compatible with renormalization. As a result, the counterterms and the renormalized Feynman amplitudes automatically satisfy the Ward identities, which leads in particular to the well-known identity $Z_1=Z_2$.
- http://arxiv.org/abs/hep-th/0602126 - preprint: The Hopf algebra of Feynman graphs in QED