Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-02-13
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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