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

Phi-Psi model for Electrodynamics in dielectric media: exact quantisation in the Heisenberg representation