  We study the electron as a system composed by an electron and a photon, using
lowest order perturbation theory. We derive the leading-twist
transverse-momentum-dependent distribution functions for both the electron and
photon in the dressed electron, thereby offering a three-dimensional
description of the dressed electron in momentum space. To obtain the
distribution functions, we apply both the formalism of light-front wave
function overlap representation and the diagrammatic approach. We perform the
calculations both in light-cone gauge and Feynman gauge, and we present a
detailed discussion of the role of the Wilson lines to obtain gauge-independent
results. We provide numerical results and plots for many of the computed
distributions.
