Flow-oriented perturbation theory

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 (digraphs). FOPT is coordinate space analogue of time-ordered and loop-tree duality, but it has the advantage having combinatorial canonical rules, combined with simplified $i\varepsilon$ dependence resulting integrals. Moreover, novel digraph-based representation for S-matrix. The associated integrals involve Fourier transform flow polytope. Due this polytope's properties, our S-matrix exhibits manifest infrared singularity factorization on per-diagram level. Our findings reveal an interesting interplay between spurious singularities transforms polytopes.