Obtaining fully polarised amplitudes in gauge invariant form

We describe progress applying the $\mathit{\text{Worldline}}\mathit{\text{Formalism}}$ 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.