Lifshitz formula for the Casimir force and the Gelfand-Yaglom theorem

Details Lifshitz formula for the Casimir force and the Gelfand-Yaglom theorem Lifshitz formula for the Casimir force and the Gelfand-Yaglom theorem

2011-07-12

arxiv.org/abs/1107.2357v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 1 figure

Scientific paper

We provide a Quantum Field Theory derivation of Lifshitz formula for the Casimir force due to a fluctuating real scalar field in $d+1$ dimensions. The field is coupled to two imperfect, thick, plane mirrors, which are modeled by background potentials localized on their positions. The derivation proceeds from the calculation of the vacuum energy in the Euclidean version of the system, reducing the problem to the evaluation of a functional determinant. The latter is written, via Gelfand-Yaglom's formula, in terms of functions depending on the structure of the potential describing each mirror; those functions encode the properties which are relevant to the Casimir force and are the reflection coefficients evaluated at imaginary frequencies.

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