Feynman Diagrams as Computational Graphs

arXiv:2403.18840v1 Announce Type: cross
Abstract: We propose a computational graph representation of high-order Feynman diagrams in Quantum Field Theory (QFT), applicable to any combination of spatial, temporal, momentum, and frequency domains. Utilizing the Dyson-Schwinger and parquet equations, our approach effectively organizes these diagrams into a fractal structure of tensor operations, significantly reducing computational redundancy. This approach not only streamlines the evaluation of complex diagrams but also facilitates an efficient implementation of the field-theoretic renormalization scheme, crucial for enhancing perturbative QFT …

abstract arxiv combination computational cond-mat.str-el cs.lg diagrams domains feynman fractal graph graph representation graphs hep-ph hep-th operations parquet physics.comp-ph quantum redundancy representation spatial temporal tensor theory type