Numerical calculation of Casimir forces

Abstract

In this thesis a set of regularized boundary integral equation are introduced that can be used to calculate the Casimir force induced by a two dimensional scalar field. The boundary integral method is compared to the functional integral method and mode summation where possible. Comparisons are done for the case of two parallel plates, two concentric circles and two adjacent circles.

The results indicate that the boundary integral method correctly predicts the geometry dependence of the Casimir force on the test problems, but that its value is missing a factor of two compared to the functional integral method and mode summation. After applying various validation procedures on the numerical implementation including a powerful test based on artificial sources, it is concluded that with high probability the missing factor of two is lost somewhere in the theory leading up to the regularized boundary integral equations.