  We examine the non-perturbative gauge dependence of arbitrary configuration
space fermion correlators in quantum electrodynamics (QED). First, we study the
dressed electron propagator (allowing for emission or absorption of any number
of photons along a fermion line) using the first quantised approach to quantum
field theory and analyse its gauge transformation properties induced by virtual
photon exchange. This is then extended to the $N$-point functions where we
derive an exact, generalised version of the fully non-perturbative
Landau-Khalatnikov-Fradkin (LKF) transformation for these correlators. We
discuss some general aspects of application in perturbation theory and
investigate the structure of the LKF factor about $D = 2$ dimensions.
