Generalised LKF transformations in spinor QED

We build upon seminal works by Landau, Khalatnikov and Fradkin (LKF) that describe the transformation of particle propagators induced by changing the gauge of virtual (loop) photons in quantum electrodynamics. Using the string-inspired first quantised approach to quantum field theory we explain how this can be generalised to uncover the exact, fully non-perturbative gauge dependence of arbitrary particle correlation functions in scalar and spinor QED for linear covariant gauges. Although these transformations are most naturally expressed in position space, we shall discuss how they can be passed to momentum space and give some examples of interest to the Schwinger model. Finally, we will describe how the transformation is realised order by order in the perturbative expansion with a focus on application to the scattering of photons off the particle lines.