The Hopf algebra of Feynman graphs in QED

Details The Hopf algebra of Feynman graphs in QED The Hopf algebra of Feynman graphs in QED

2006-02-13

arxiv.org/abs/hep-th/0602126v2

Lett.Math.Phys.77:265-281,2006

Physics

High Energy Physics

High Energy Physics - Theory

13 pages. Latex, uses feynmp. Minor corrections; to appear in LMP

Scientific paper

10.1007/s11005-006-0092-4

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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