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

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 $ϕ$ and the role of the polarization field is played by a further scalar field $ψ$. 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.

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