Feynman Integrals Meet Second-Order Partial Differential Equations

by Hantian Zhang (CERN)

Tuesday 8 Dec 2026, 10:45 → 11:45 Europe/Berlin

TUM, Physics Department, Garching

In this talk, I will discuss the recently proposed 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. I will also discuss future prospects and developments of this method.