Obtaining fully polarised amplitudes in gauge invariant form

TL;DR

This paper applies the Worldline Formalism to derive compact, gauge-invariant amplitudes for multi-photon fermion scattering, enhancing computational efficiency in quantum field theory.

Contribution

It introduces a novel application of the Worldline Formalism to obtain fully polarized, gauge-invariant amplitudes for complex scattering processes.

Findings

Derivation of compact, gauge-invariant scattering amplitudes

Demonstration of the formalism's efficiency at multi-loop order

Advancement in calculating multi-photon processes in QED

Abstract

We describe progress applying the \textit{Worldline Formalism} of quantum field theory to the fermion propagator dressed by $N$-photons to study multi-linear Compton scattering processes, explaining how this approach -- whose calculational advantages are well-known at multi-loop order -- yields compact and manifestly gauge invariant scattering amplitudes.