Path integral quantization of the relativistic Hopfield model
arXiv:1601.01677 · doi:10.1103/PhysRevD.93.065020
Abstract
The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path integral formalism. In particular we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.
arXiv comment16 pages
References in corpus (8)
- Fiber-optical analogue of the event horizon
- Equivalence of Faddeev-Jackiw and Dirac approaches for gauge theories
- Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse
- Blackbody emission from light interacting with an effective moving dispersive medium
- Spontaneous quantum emission from analog white holes in a nonlinear optical medium
- Faddeev-Jackiw quantization and the path integral
- Perturbative photon production in a dispersive medium
- Exact quantisation of the relativistic Hopfield model