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- W2000522832 abstract "Using the Proca equations, which are appropriate when the photon has a finite mass m, the force between two perfectly conducting parallel slabs, each of width N, and separated by a distance 2L, is calculated. The approach is through the L-dependence of the combined quantum zero-point energies (ZPE) of all the normal modes of the system. The general results are evaluated in a regime with λ = mL ⪡ 1 and ν = mN ⪡ 1. The two leading finite-mass corrections are of relative order λ2 and λ4 log λ; both stem from essentially kinematic corrections to the modes already present in the Maxwell case m = 0, and having a discrete spectrum between the slabs. There are further corrections of relative order λ4 and (for N ⪢ L) λ4log(NL), the last stemming from dynamically new (penetrating) modes present only for m ≠ 0, to which even perfect conductors are almost transparent, and which possess a continuous spectrum. The calculation has byproducts which may prove more fruitful than the results themselves. These are: (i) A complete analysis of the Proca normal-mode structure for parallel-plane geometry, the first such complete analysis, as far as it is known, for any system. A special role is played by the component A2 of the vector potential normal to the slabs, which is unique amongst the potentials and fields in that not only A2 but also ∂A2∂z are continuous across the surfaces; this governs the classification of the modes, and effectively reduces the analysis of the penetrating modes to that for a scalar field. (ii) A clearer understanding of the way in which the total ZPE of continuum modes varies with system parameters like L and N. (iii) Requisite for (ii), a statement of Levinson's theorem in one dimension, which for even-parity modes displays unfamiliar features." @default.
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- W2000522832 date "1985-07-01" @default.
- W2000522832 modified "2023-09-23" @default.
- W2000522832 title "The Casimir effect with finite-mass photons" @default.
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- W2000522832 doi "https://doi.org/10.1016/0003-4916(85)90162-9" @default.
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