We investigate Feynman graphs and their Feynman rules from the viewpoint of graph complexes. We focus on the interplay between graph homology, Hopf-algebraic structures on Feynman graphs and the analytic structure of their associated integrals. Furthermore, we discuss the appearance of cubical complexes where the differential is formed by reducing internal edges and by putting edge-propagators on the mass-shell.

中文翻译：

---

图复形和费曼规则

我们从图复形的角度研究费曼图及其费曼规则。我们关注图同源性、费曼图上的 Hopf 代数结构及其相关积分的解析结构之间的相互作用。此外，我们讨论了立方体复合体的外观，其中微分是通过减少内部边缘并将边缘传播器放在质量壳上而形成的。