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arXiv · 1512.08739

Exact quantisation of the relativistic Hopfield model

F. Belgiorno·S. L. Cacciatori·F. Dalla Piazza·M. Doronzo
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Abstract

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields. The matter fields are represented by a mesoscopic polarization field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalized Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.

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F. Belgiorno, S. L. Cacciatori, F. Dalla Piazza, M. Doronzo. 2015-12-29. Exact quantisation of the relativistic Hopfield model. https://doi.org/10.1016/j.aop.2016.09.001

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