  We investigate the quantisation in the Heisenberg representation of a
relativistically covariant version of the Hopfield model for dielectric media,
which entails the interaction of the quantum electromagnetic field with the
matter dipole fields. The matter fields are represented by a mesoscopic
polarization field. A full quantisation of the model is provided in a covariant
gauge, with the aim of maintaining explicit relativistic covariance. Breaking
of the Lorentz invariance due to the intrinsic presence in the model of a
preferred reference frame is also taken into account. Relativistic covariance
forces us to deal with the unphysical (scalar and longitudinal) components of
the fields, furthermore it introduces, in a more tricky form, the well-known
dipole ghost of standard QED in a covariant gauge. In order to correctly
dispose of this contribution, we implement a generalized Lautrup trick.
Furthermore, causality and the relation of the model with the Wightman axioms
are also discussed.
