Graph complexes and Feynman rules

TL;DR

This paper explores the relationship between Feynman graphs, graph complexes, and homological structures, revealing new insights into their topological and combinatorial properties in quantum field theory.

Contribution

It introduces a novel perspective by analyzing Feynman graphs through the lens of graph complexes and homology, highlighting the emergence of cubical complexes in specific reductions.

Findings

Identification of cubical complexes in graph reductions

Connection between graph homology and Feynman rules

New topological insights into Feynman graph structures

Abstract

We investigate Feynman graphs and their Feynman rules from the viewpoint of graph complexes. We focus on graph homology and on the appearance of cubical complexes when either reducing internal edges or when removing them by putting them on the massshell.