  In this and companion papers, we show that quantum field theories with gauge
symmetries permit a broader class of classical dynamics than typically assumed.
In this article, we show that the quantization of electromagnetism permits the
existence of classical electric field states that do not obey Gauss's law.
These states are gauge invariant and their time evolution can be consistently
described using the Schr\"{o}dinger equation. The time evolution of these
states is such that at the classical level, the full set of Maxwell's equations
would appear to hold, with the physical effects of these states being
attributable to an auxiliary, static ``shadow'' charge density with no internal
degrees of freedom. This density could affect the dynamics of charged particles
in our universe and it may thus be of observational interest.
