  In this paper, we consider the Maxwell-Dirac system in 3 dimension under zero
magnetic field. We prove the global well-posedness and modified scattering for
small solutions in the weighted Sobolev class. Imposing the Lorenz gauge
condition, (and taking the Dirac projection operator), it becomes a system of
Dirac equations with Hartree type nonlinearity with a long range potential as
$|x|^{-1} $. We perform the weighted energy estimates. In this procedure, we
have to deal with various resonance functions that stem from the Dirac
projections. We use the spacetime resonance argument of
Germain-Masmoudi-Shatah, as well as the spinorial null-structure. On the way,
we recognize a long range interaction which is responsible for a logarithmic
phase correction in the modified scattering statement.
