The Hopf Algebra of Feynman Graphs in Quantum Electrodynamics
The Hopf Algebra of Feynman Graphs in Quantum Electrodynamics
复制标题
量子电动力学中费曼图的霍普夫代数
DOI：
10.1007/s11005-006-0092-4
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发表时间：
2006
影响因子：
1.2
通讯作者：
W. D. Suijlekom
中科院分区：
文献类型：
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作者：
W. D. Suijlekom
本文报道量子电动力学重整化理论的Hopf代数描述。Ward-Takahashi（WT）恒等式在量子电动力学Feynman图的（交换）Hopf代数上实现为线性关系.这些关系与Hopf代数结构的相容性是WT恒等式与重整化相容的物理事实的数学表述。结果，反项和重正化的费曼振幅自动满足WT恒等式，这特别导致众所周知的恒等式Z1 = Z2。
We report on the Hopf algebraic description of renormalization theory of quantum electrodynamics. The Ward–Takahashi (WT) identities are implemented as linear relations on the (commutative) Hopf algebra of Feynman graphs of quantum electrodynamics. 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 Z1 = Z2.