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arXiv · hep-th/0602126

The Hopf algebra of Feynman graphs in QED

Walter van Suijlekom
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Abstract

We report on the Hopf algebraic description of renormalization theory of quantum electrodynamics. The Ward-Takahashi identities are implemented as linear relations on the (commutative) 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 WT-identities are compatible with renormalization. As a result, the counterterms and the renormalized Feynman amplitudes automatically satisfy the WT-identities, which leads in particular to the well-known identity $Z_1=Z_2$.

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Walter van Suijlekom. 2006-05-22. The Hopf algebra of Feynman graphs in QED. https://doi.org/10.1007/s11005-006-0092-4

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