On overlapping Feynman (sub)graphs

Abstract

We discuss, on general grounds, how two subgraphs of a given Feynman graph can overlap with each other. For this, we use the notion of connecting and returning lines that describe how any subgraph is inserted within the original graph. This, in turn, allows us to derive "non-overlap" theorems for one-particle-irreducible subgraphs with $2$, $3$ and $4$ external legs. As an application, we provide a simple justification of the skeleton expansion for vertex functions with more than five legs, in the case of scalar field theories. We also discuss how the skeleton expansion can be extended to other classes of graphs.

arXiv comment28 pages, 5 figures

References in corpus (9)

• Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model
• n-Particle irreducible effective action techniques for gauge theories
• On Overlapping Divergences
• C_{T} and C_{J} up to next-to-leading order in 1/N in the Conformally Invariant O(N) Vector Model for 2<d<4
• Insertion and Elimination: the doubly infinite Lie algebra of Feynman graphs
• Techniques for n-Particle Irreducible Effective Theories
• Operator Product Expansions and Consistency Relations in a O(N) Invariant Fermionic CFT for 2<d<4
• Renormalization without infinities
• Skeleton expansion and large spin bootstrap for ${\varphi }^3$ theory

Cited by in corpus (1)

• Functional renormalization group and 2PI effective action formalism