  A Hamiltonian field theory for the macroscopic Maxwell equations with fully
general polarization and magnetization is stated in the language of
differential forms. The precise procedure for translating the vector calculus
formulation into differential forms is discussed in detail. We choose to
distinguish between straight and twisted differential forms so that all
integrals be taken over densities (i.e. twisted top forms). This ensures that
the duality pairings, which are stated as integrals over densities, are
orientation independent. The relationship between functional differentiation
with respect to vector fields and with respect to differential forms is
established using the chain rule. The theory is developed such that the Poisson
bracket is metric and orientation independent with all metric dependence
contained in the Hamiltonian. As is typically seen in the exterior calculus
formulation of Maxwell's equations, the Hodge star operator plays a key role in
modeling the constitutive relations. As a demonstration of the kind of
constitutive models this theory accommodates, the paper concludes with several
examples.
