  We investigate the quantization in the Heisenberg representation of a model
which represents a simplification of the Hopfield model for dielectric media,
where the electromagnetic field is replaced by a scalar field $\phi$ and the
role of the polarization field is played by a further scalar field $\psi$. The
model, which is quadratic in the fields, is still characterized by a nontrivial
physical content, as the physical particles correspond to the polaritons of the
standard Hopfield model of condensed matter physics. Causality is also taken
into account and a discussion of the standard interaction representation is
also considered.
