Integration techniques for worldline integrals

TL;DR

This paper reviews advanced integration techniques for worldline integrals in quantum electrodynamics, highlighting challenges and current methods for calculating complex Feynman diagram representations.

Contribution

It summarizes the state-of-the-art in worldline integral techniques, emphasizing their application to QED in vacuum and external fields.

Findings

Overview of worldline formalism advantages

Identification of integration challenges in QED

Summary of current solution approaches

Abstract

The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing mathematical algorithms are of little help. Here I will summarize the state-of-the-art of worldline integration focusing on examples from QED in vacuum and in constant external fields.