Using boundary methods to compute the Casimir energy

F.C. LOMBARDO, F.D. MAZZITELLI , AND P.I. VILLAR

The University of Oklahoma Norman, OK USA

Conferencia; Ninth Conference on QUANTUM FIELD THEORY UNDER THE INFLUENCE OF EXTERNAL CONDITIONS; 2009

We discuss new approaches to compute numerically the Casimir interactionenergy for waveguides of arbitrary section, based on the boundary methodstraditionally used to compute eigenvalues of the 2D Helmholtz equation. Thesemethods are combined with the Cauchy’s theorem in order to perform thesum over modes. As an illustration, we describe a point-matching techniqueto compute the vacuum energy for waveguides containing media with differentpermittivities. We present explicit numerical evaluations for perfect conductingsurfaces in the case of concentric corrugated cylinders and a circular cylinderinside an elliptic one.