  The operator ${\bf S}$ in Fock space which describes the scattering and
particle production processes in an external time-dependent electromagnetic
potential $A$ can be constructed from the one-particle S-matrix up to a
physical phase $\lambda [A]$. In this work we determine this phase for $QED$ in
(2+1) dimensions, by means of causality, and show that no ultraviolet
divergences arise, in contrast to the usual formalism of $QED$.
