Insulating the Vacuum. Calculating the Casimir force using the boundary integral method with von Neumann boundary conditions

Abstract

In 2012, a new method for calculating the Casimir force between compact objects was developed, expressing the force in terms of a boundary integral equation. The case of perfectly conducting objects with Dirichlet boundary conditions in two dimensions was treated by Isak Kilen. The method was later extended to three dimensions by Karl Øyvind Mikalsen.

The contribution of this thesis will be to develop the method in two dimensions for the case when the objects are perfectly insulating, meaning von Neumann boundary conditions. A formula for the Casimir force in terms of a boundary integral problem is derived and shown to correctly predict the force between two parallel plates, except for a missing factor of 2 that was also observed for Dirichlet boundary conditions. The developed formula contains a coefficient that is dependent on the regularization scheme used, and it is not clear whether this coefficient is geometry-independent.