  The Shale-Stinespring Theorem (1965) together with Ruijsenaar's criterion
(1977) provide a necessary and sufficient condition for the implementability of
the evolution of external field quantum electrodynamics between constant-time
hyperplanes on standard Fock space. The assertion states that an implementation
is possible if and only if the spacial components of the external
electromagnetic four-vector potential $A_\mu$ are zero. We generalize this
result to smooth, space-like Cauchy surfaces and, for general $A_\mu$, show how
the second-quantized Dirac evolution can always be implemented as a map between
varying Fock spaces. Furthermore, we give equivalence classes of polarizations,
including an explicit representative, that give rise to those admissible Fock
spaces. We prove that the polarization classes only depend on the tangential
components of $A_\mu$ w.r.t. the particular Cauchy surface, and show that they
behave naturally under Lorentz and gauge transformations.
