  The possibility of electron-positron pair creation by an electric field is
studied by using only those methods in field theory the predictions of which
are confirmed experimentally. These methods include the perturbative method of
quantum electrodynamics and the bases of classical electrodynamics. Such an
approach includes the back reaction. It is found that the vacuum is always
stable, in the sense that pair creation, if occurs, cannot be interpreted as a
decay of the vacuum, but rather as a decay of the source of the electric field
or as a process similar to bremsstrahlung. It is also found that there is no
pair creation in a static electric field, because it is inconsistent with
energy conservation. The non-perturbative aspects arising from the Borel
summation of a divergent perturbative expansion are discussed. It is argued
that the conventional methods that predict pair creation in a classical
background electric field cannot serve even as approximations. The analogy with
the possibility of particle creation by a gravitational field is qualitatively
discussed.
