Worldline integration of photon amplitudes

TL;DR

This paper discusses advancements in applying the worldline formalism, inspired by string theory, to compute photon amplitudes at one and two loops, addressing complex integration challenges in quantum field theory calculations.

Contribution

It provides progress on using the worldline formalism for photon amplitude calculations, tackling non-standard integration problems beyond traditional Feynman diagram methods.

Findings

Developed new integral representations for photon amplitudes

Addressed complex integration challenges in loop calculations

Enhanced computational techniques for quantum field theory amplitudes

Abstract

It has been known for many years that methods inspired by string theory, such as the worldline formalism, allow one to write down integral representations that combine large numbers of Feynman diagrams of different topologies. However, to make this fact useful for state-of-the-art calculations one has to confront non-standard integration problems where neither the known integration techniques for Feynman diagrams nor algebraic manipulation programs are of much help. Here I will give a progress report on this long-term project focussing on photon amplitudes at one and two loops, in vacuum and in external fields.