Eur. Phys. J. C (2016) 76: 308
https://doi.org/10.1140/epjc/s10052-016-4146-1

Regular Article - Theoretical Physics

model for electrodynamics in dielectric media: exact quantisation in the Heisenberg representation

¹ Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo 32, 20133, Milano, Italy
² INdAM-GNFM, Milano, Italy
³ Department of Science and High Technology, Università dell’Insubria, Via Valleggio 11, 22100, Como, Italy
⁴ INFN sezione di Milano, via Celoria 16, 20133, Milano, Italy
⁵ Dipartimento di Matematica, Università “La Sapienza”, Piazzale A. Moro 2, 00185, Roma, Italy

^* e-mail: f.dallapiazza@gmail.com

Received: 6 April 2016
Accepted: 17 May 2016
Published online: 2 June 2016

Abstract

We investigate the quantisation 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 and the role of the polarisation field is played by a further scalar field . The model, which is quadratic in the fields, is still characterised by a non-trivial 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.