Year: 2026
Type: preprint
Abstract: We propose a second-order partial differential equation method to solve multi-loop Feynman integrals as an equilibrium problem. As a proof-of-concept demonstration, we perform a Galerkin discretization of the corresponding variational form and employ the finite element method to compute two-loop four-point Feynman integrals. This method can solve the integral over a broad region of multi-dimensional phase space once and for all. This work establishes a new connection between perturbative quantum field theory and modern partial differential equation methods, with the potential to streamline a wide range of phenomenological applications.
Source: arXiv (Cornell University)
Authors: Chen, Xiang, Zhang, Hantian
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170041640