Worldline representation of multiloop amplitudes in quantum electrodynamics
arXiv:2607.13321
The paper reviews the worldline formalism for quantum electrodynamics and its application to multiloop calculations, highlighting recent results for the two‑loop vacuum polarization in scalar QED and related master integral formulas.
Abstract
The worldline approach to quantum electrodynamics allows one to construct integral representations combining large numbers of Feynman diagrams. Here I review the state-of-the-art of a long-term effort to make this fact useful for actual multiloop calculations, such as of the scalar and spinor QED vacuum polarization functions and the electron anomalous magnetic moment. After a short historical introduction, and a discussion of the non-standard mathematical challenges involved, I focus on a recent calculation of the two-loop vacuum polarisation in scalar QED and some master integral formulas obtained in this context.
13 pages, 8 figures, talk given by Christian Schubert at Loops and Legs in Quantum Field Theory (LL2026), April 12-17, 2026, Bayreuth, Germany