Deforming the vacuum. On the physical origin and numerical calculation of the Casimir effect.

Abstract

A new method for calculating the Casimir force between compact objects was introduced in May 2012 by Per Jakobsen and Isak Kilen. In this method a regularization procedure is used to reduce the pressure to the solution of an integral equation defined on the boundaries of the objects. In this thesis the method is further developed by extending from a 2D to a 3D massless scalar field, subject to Dirichelet boundary conditions on the boundaries of the objects. The method is implemented numerically and tested on configurations consisting of plates, spheres and ellipsoids. We compare the method to the functional integral method and the method of mode summation where possible.

Our results are in accordance with what I. Kilen found; the method correctly predicts the geometry dependence of the Casimir force, but the size of the force is off by a factor of two.