The Soft Wall Model of the Casimir Effect

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Whisler, Colin M.; Murray, Steven
Casimir effect; vacuum energy; pressure anomaly; soft-wall model
thesis / dissertation description
In this paper, we examine the Casimir interaction between a scalar field and a boundary analogous to a conducting wall with some small but finite skin depth to electromagnetic radiation with the goal of calculating the energy density and pressure. We model the wall as a “soft wall” where the potential is given by a monomial function of arbitrary degree. The soft-wall approximation is a useful model because it eliminates some of the divergent terms that arise during the traditional approach to the subject. For the region outside the wall, we show that the principle of virtual work holds, not just formally for the infinite energy, but regardless of the regularization method used to obtain finite interaction energies and pressures. Furthermore, we lay the groundwork to prove this property inside the wall. We present improvements and extensions of prior work in the field by adjusting the approximations used to increase accuracy as well as calculating the pressure. The solution can be applied to the hard-wall case by adjusting the parameters, allowing us to calculate the desired quantities without having to contend with divergences.