Dispersion and Loss in a Hopfield Dielectric

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Abstract
We develop a fully canonical quantization scheme for the electromagnetic field in linear dielectrics, including dispersion and losses. This scheme is based on the Hopfield model of a dielectric, where the medium is represented by a number of interacting matter fields. The relationship between dispersion and absorption, as expressed by the Kramers-Kronig relations, is explicitly derived. We obtain simple expressions for the electromagnetic field in the medium and show how a complex wave vector can be derived, even in the case of a quantized field.