Angles, Scales and Parametric Renormalization
Angles, Scales and Parametric Renormalization
复制标题
角度、比例和参数重整化
DOI：
10.1007/s11005-013-0625-6
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发表时间：
2011
影响因子：
1.2
通讯作者：
D. Kreimer
中科院分区：
文献类型：
--
作者：
F. Brown;D. Kreimer
We discuss the structure of renormalized Feynman rules. Regarding them as maps from the Hopf algebra of Feynman graphs to $${\mathbb{C}}$$ originating from the evaluation of graphs by Feynman rules, they are elements of a group $${G=\mathrm{Spec}_{\mathrm{Feyn}}(H)}$$ . We study the kinematics of scale and angle-dependence to decompose G into subgroups $${G_{\mathrm{\makebox{1-s}}}}$$ and $${G_{\mathrm{fin}}}$$ . Using parametric representations of Feynman integrals, renormalizability and the renormalization group underlying the scale dependence of Feynman amplitudes are derived and proven in the context of algebraic geometry.
We discuss the structure of renormalized Feynman rules. Regarding them as maps from the Hopf algebra of Feynman graphs to $${\mathbb{C}}$$ originating from the evaluation of graphs by Feynman rules, they are elements of a group $${G=\mathrm{Spec}_{\mathrm{Feyn}}(H)}$$ . We study the kinematics of scale and angle-dependence to decompose G into subgroups $${G_{\mathrm{\makebox{1-s}}}}$$ and $${G_{\mathrm{fin}}}$$ . Using parametric representations of Feynman integrals, renormalizability and the renormalization group underlying the scale dependence of Feynman amplitudes are derived and proven in the context of algebraic geometry.