  The one-loop effective action of quantum electrodynamics in four dimensions
is shown to be controlled by the Euclidean Dirac propagator $G$ in a background
potential. After separating the photon self-energy and photon-photon scattering
graphs from the effective action the remainder is known to be the logarithm of
an entire function of the electric charge of order 4 under mild regularity
assumptions on the potential. This input together with QED's lack of an
ultrastable vacuum constrain the strong field behavior of $G$. It is shown that
$G$ vanishes in the strong field limit. The relevance of this result to the
decoupling of QED from the remainder of the electroweak model for large
amplitude variations of the Maxwell field is discussed.
