  We consider the non-interacting source-free Maxwell field, described both in
terms of the vector potential and the field strength. Starting from the
classical field theory on contractible globally hyperbolic spacetimes, we
extend the classical field theory to general globally hyperbolic spacetimes in
two ways to obtain a "universal" theory and a "reduced" theory. The quantum
field theory in terms of the unital $*$-algebra of the smeared quantum field is
then obtained by an application of a suitable quantisation functor. We show
that the universal theories fail local covariance and dynamical locality owing
to the possibility of having non-trivial radicals in the classical and
non-trivial centres in the quantum case. The reduced theories are both locally
covariant and dynamically local. These models provide new examples relevant to
the discussion of how theories should be formulated so as to describe the same
physics in all spacetimes.
