  An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics
is just one instance of a variety of theories for which the name
electrodynamics is justified. They all have in common that their fundamental
input are Maxwell's equations $\textrm{d} F = 0$ (or $F = \textrm{d} A$) and
$\textrm{d} H = J$ and a constitutive law $H = # F$ which relates the field
strength two-form $F$ and the excitation two-form $H$. A local and linear
constitutive law defines what is called local and linear pre-metric
electrodynamics whose best known application are the effective description of
electrodynamics inside media including, e.g., birefringence. We analyze the
classical theory of the electromagnetic potential $A$ before we use methods
familiar from mathematical quantum field theory in curved spacetimes to
quantize it in a locally covariant way. Our analysis of the classical theory
contains the derivation of retarded and advanced propagators, the analysis of
the causal structure on the basis of the constitutive law (instead of a metric)
and a discussion of the classical phase space. This classical analysis sets the
stage for the construction of the quantum field algebra and quantum states.
Here one sees, among other things, that a microlocal spectrum condition can be
formulated in this more general setting.
