Generalized Planar Feynman Diagrams: Collections
Francisco Borges, Freddy Cachazo

TL;DR
This paper introduces a generalization of planar Feynman diagrams called metric tree arrangements, providing a new geometric framework for computing amplitudes in scalar theories.
Contribution
It proposes metric tree arrangements as a natural extension of Feynman diagrams and develops a method to generate all planar collections from a canonical initial collection.
Findings
Defines planar collections of Feynman diagrams with compatibility conditions.
Shows how to generate all planar collections from a single initial collection.
Provides a method to compute generalized biadjoint amplitudes as integrals over metric spaces.
Abstract
Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each degeneration of a tree leads to a single planar neighbor. Amplitudes are computed as an integral over the space of metrics where edge lengths are Schwinger parameters. In this work we propose that a natural generalization of Feynman diagrams is provided by what are known as metric tree arrangements. These are collections of metric trees subject to a compatibility condition on the metrics. We introduce the notion of planar collections of Feynman diagrams and argue that using planarity one can generate all planar collections starting from any one. Moreover, we identify a canonical initial collection for all . Generalized biadjoint amplitudes,…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
