QED commutation relations for inhomogeneous Kramers-Kronig dielectrics
arXiv:quant-ph/9803031 · doi:10.1103/PhysRevA.58.700
Abstract
Recently a quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium has been developed and applied to a system consisting of two infinite half-spaces with a common planar interface (H.T. Dung, L. Knoell, and D.-G. Welsch, Phys. Rev. A 57, in press). Here we show that the scheme, which is based on the classical Green-tensor integral representation of the electromagnetic field, applies to any inhomogeneous medium. For this purpose we prove that the fundamental equal-time commutation relations of QED are preserved for an arbitrarily space-dependent, Kramers--Kronig consistent permittivity. Further, an extension of the quantization scheme to linear media with bounded regions of amplification is given, and the problem of anisotropic media is briefly addressed.
15 pages
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