Flow-oriented perturbation theory

TL;DR

This paper presents flow-oriented perturbation theory, a new diagrammatic method in quantum field theory that simplifies calculations and reveals infrared singularity factorization through a novel digraph-based S-matrix representation.

Contribution

It introduces flow-oriented perturbation theory with a new digraph-based S-matrix and a polytope Fourier transform approach, enhancing diagrammatic clarity and singularity analysis.

Findings

Manifest infrared singularity factorization at the diagram level

Simplified $i\varepsilon$ dependence in integrals

Novel digraph representation for the S-matrix

Abstract

We introduce a new diagrammatic approach to perturbative quantum field theory, which we call flow-oriented perturbation theory (FOPT). Within it, Feynman graphs are replaced by strongly connected directed graphs (digraphs). FOPT is a coordinate space analogue of time-ordered perturbation theory and loop-tree duality, but it has the advantage of having combinatorial and canonical Feynman rules, combined with a simplified $i\varepsilon$ dependence of the resulting integrals. Moreover, we introduce a novel digraph-based representation for the S-matrix. The associated integrals involve the Fourier transform of the flow polytope. Due to this polytope's properties, our S-matrix representation exhibits manifest infrared singularity factorization on a per-diagram level. Our findings reveal an interesting interplay between spurious singularities and Fourier transforms of polytopes.