Weak Coupling Casimir Energies for Finite Plate Configurations

Abstract

We derive and use an extremely simplified formula for the interaction Casimir energy for two separate bodies in the weak coupling regime for massless scalar fields. We derive closed form solutions for a general arrangement of two $\delta$-function plates finite in one direction and infinite in another. We examine the situation of two parallel plates finite in both transverse directions.

10pages 6 figures

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• Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
• A perturbative approach to calculating the Casimir force in fluctuating scalar and vector fields
• Vacuum fluctuations in the presence of nonlinear boundary conditions
• On the Casimir effect from the zero-point energy: A tangential force and its properties