  The shape of the electron is studied using lowest-order perturbation theory.
Quantities used to probe the structure of the proton: form factors, generalized
parton distributions, transverse densities, Wigner distributions and the
angular momentum content are computed for the electron-photon component of the
electron wave function. The influence of longitudinally polarized photons,
demanded by the need for infrared regularization via a non-zero photon mass, is
included. The appropriate value of the photon mass depends on experimental
conditions, and consequently the size of the electron (as defined by the slope
of its Dirac form factor) bound in a hydrogen atom is found to be about four
times larger than when the electron is free. The shape of the electron, as
determined from the transverse density and generalized parton distributions is
shown to not be round, and the free electron is shown to be far less round than
the bound electron. An electron distribution function (analogous to the quark
distribution function) is defined, and that of the bound electron is shown to
be suppressed compared to that of the free electron. If the relative transverse
momentum of the virtual electron and photon is large compared with the electron
mass, the virtual electron and photon each carry nearly the total angular
momentum of the physical electron (1/2), with the orbital angular momentum
being nearly (-1/2). Including the non-zero photon mass leads to the
suppression of end-point contributions to form factors. Implications for proton
structure and color transparency are discussed.
