dorsal/arxiv
View SchemaThree-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics
| Authors | Ho Trung Dung, L. Knoell, D. -G. Welsch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9711039 |
| URL | https://arxiv.org/abs/quant-ph/9711039 |
| DOI | 10.1103/PhysRevA.57.3931 |
Abstract
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers-Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional current- and charge-density operator fields in order to take into account the noise associated with the dissipation in the medium. It is shown that the equal-time commutation relations between the fundamental electromagnetic fields $\hat E$ and $\hat B$ and the potentials $\hat A$ and $\hat \phi$ in the Coulomb gauge can be expressed in terms of the Green tensor of the classical problem. From the Green tensors for bulk material and an inhomogeneous medium consisting of two bulk dielectrics with a common planar interface it is explicitly proven that the well-known equal-time commutation relations of QED are preserved.
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"abstract": "A quantization scheme for the phenomenological Maxwell theory of the full\nelectromagnetic field in an inhomogeneous three-dimensional, dispersive and\nabsorbing dielectric medium is developed. The classical Maxwell equations with\nspatially varying and Kramers-Kronig consistent permittivity are regarded as\noperator-valued field equations, introducing additional current- and\ncharge-density operator fields in order to take into account the noise\nassociated with the dissipation in the medium. It is shown that the equal-time\ncommutation relations between the fundamental electromagnetic fields $\\hat E$\nand $\\hat B$ and the potentials $\\hat A$ and $\\hat \\phi$ in the Coulomb gauge\ncan be expressed in terms of the Green tensor of the classical problem. From\nthe Green tensors for bulk material and an inhomogeneous medium consisting of\ntwo bulk dielectrics with a common planar interface it is explicitly proven\nthat the well-known equal-time commutation relations of QED are preserved.",
"arxiv_id": "quant-ph/9711039",
"authors": [
"Ho Trung Dung",
"L. Knoell",
"D. -G. Welsch"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.57.3931",
"title": "Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics",
"url": "https://arxiv.org/abs/quant-ph/9711039"
},
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