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

TL;DR

This paper presents an exact quantization of a simplified scalar field model for dielectric media in the Heisenberg representation, capturing polariton physics and causality considerations.

Contribution

It introduces a quadratic scalar field model that simplifies the Hopfield model, enabling exact quantization and analysis of polariton dynamics in dielectric media.

Findings

Exact quantization achieved in the Heisenberg representation.

Model reproduces key physical features of polaritons.

Discussion of causality and interaction representation included.

Abstract

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.