Exact quantisation of the relativistic Hopfield model
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, represented by a mesoscopic polarisation 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 generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.
- Publication:
-
Annals of Physics
- Pub Date:
- November 2016
- DOI:
- 10.1016/j.aop.2016.09.001
- arXiv:
- arXiv:1512.08739
- Bibcode:
- 2016AnPhy.374..338B
- Keywords:
-
- Hopfield model;
- Heisenberg representation;
- Polariton;
- QED;
- Mathematical Physics;
- High Energy Physics - Theory
- E-Print:
- 24 pages