  We construct the time-evolution for the second quantized Dirac equation
subject to a smooth, compactly supported, time dependent electromagnetic
potential and identify the degrees of freedom involved. Earlier works on this
(e.g. Ruijsenaars) observed the Shale-Stinespring condition and showed that the
one-particle time-evolution can be lifted to Fock space if and only if the
external field had zero magnetic components. We scrutinize the idea, observed
earlier by Fierz and Scharf, that the time-evolution can be implemented between
time varying Fock spaces. In order to define these Fock spaces we are led to
consider classes of reference vacua and polarizations. We show that this
implementation is up to a phase independent of the chosen reference vacuum or
polarization and that all induced transition probabilities are well-defined and
unique.
