Flow-oriented perturbation theory

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 $i\epsilon$ 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.

54 pages, many figures; v2: typos corrected and discussion on renormalization added - version to appear in JHEP

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Cited by in corpus (5)

• Exposing the threshold structure of loop integrals
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Local infrared safety in time-ordered perturbation theory
• Flow Oriented Perturbation Theory
• Coordinate light-cone-ordered perturbation theory