发表机构
Physik-Institut, Universität Zürich; Theoretical Physics Department, CERN（苏黎世大学物理学院; 欧洲核子研究中心理论物理部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出用二阶偏微分方程方法求解多圈费曼积分，通过伽辽金离散化和有限元方法计算两圈四点费曼积分，能解决多维相空间广泛区域积分，建立了量子场论与偏微分方程方法新联系，利于简化应用。
AI 中文摘要
我们提出一种二阶偏微分方程方法，将求解多圈费曼积分作为一个平衡问题。作为概念验证演示，我们对相应变分形式进行伽辽金离散化，并采用有限元方法计算两圈四点费曼积分。该方法能一次性解决多维相空间广泛区域上的积分。此工作在微扰量子场论和现代偏微分方程方法之间建立了新联系，有望简化众多唯象学应用。
英文摘要
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.
Commentsv2: add appendix: naturalness of Laplacian structure
