We have obtained nonperturbative one-loop expressions
for the mean energy-momentum tensor and current
density of Dirac's field on a constant electric-like
background. One of the goals of this calculation is
to give a consistent description of back-reaction in
such a theory. Two cases of initial states are
considered: the vacuum state and the thermal equilibrium
state. First, we perform calculations for the vacuum
initial state. In the obtained expressions, we separate
the contributions due to particle creation and vacuum
polarization. The latter contributions are related to
the Heisenberg--Euler Lagrangian. Then, we study the
case of the thermal initial state. Here, we separate the
contributions due to particle creation, vacuum
polarization, and the contributions due to the work of
the external field on the particles at the initial state.
All these contributions are studied in detail, in
different regimes of weak and strong fields and low and
high temperatures. The obtained results allow us to
establish restrictions on the electric field and its
duration under which QED with a strong constant electric
field is consistent. Under such restrictions, one can
neglect the back-reaction of particles created by the
electric field. Some of the obtained results generalize
the calculations of Heisenberg--Euler for energy density
to the case of arbitrary strong electric fields.