论 Kreimer 关于费曼图的 Hopf 代数结构
高能物理 - 理论
2011-09-13 v4
摘要
我们重新考察 Kreimer 关于微扰量子场论的 Hopf 代数结构，特别着重于重叠发散。Kreimer 首先将重叠发散解缠为不相交与嵌套发散的线性组合，然后借助 Hopf 代数运算处理该线性组合。我们给出一种表述，其中 Hopf 代数运算直接定义于任意类型的发散上。我们阐明了其与 Kreimer 的 Hopf 代数的精确关系，并由此得到其原初元素的刻画。
关键词
引用
@article{arxiv.hep-th/9805098,
title = {On Kreimer's Hopf algebra structure of Feynman graphs},
author = {Thomas Krajewski and Raimar Wulkenhaar},
journal= {arXiv preprint arXiv:hep-th/9805098},
year = {2011}
}
备注
21 pages, LaTeX2e, requires feynmf package to draw Feynman graphs (see log file for additional information). Following an idea by Dirk Kreimer we introduced in the revised version a primitivator which maps overlapping divergences to primitive elements and which provides the link to the Hopf algebra of Kreimer (q-alg/9707029, hep-th/9808042). v4: error in eq (29) corrected and references updated; to appear in Eur.Phys.J. C