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Abstract: We determine the commutation relations satisfied by the quantizedelectromagnetic field in the presence of macroscopic dielectrics andconductors, with arbitrary dispersive and dissipative properties. We considerin detail the case of two plane-parallel material slabs, separated by an emptygap, and we show that at all points in the empty region between the slabs,including their surfaces, the electromagnetic fields always satisfy free-fieldcanonical equal-time commutation relations. This result is a consequence ofgeneral analyticity and fall-off properties at large frequencies satisfied bythe reflection coefficients of all real materials. It is also shown that thisresult does not obtain in the case of conductors, if the latter are modelled asperfect mirrors. In such a case, the free-field form of the commutationrelations is recovered only at large distances from the mirrors, in agreementwith the findings of previous authors. Failure of perfect-mirror boundaryconditions to reproduce the correct form of the commutation relations near thesurfaces of the conductors, suggests that caution should be used when theseidealized boundary conditions are used in investigations of proximity phenomenaoriginating from the quantized electromagnetic field, like the Casimir effect.



Author: Giuseppe Bimonte

Source: https://arxiv.org/







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