An exact evaluation of the Casimir energy in two planar models

Abstract

The method of images is used to calculate the Casimir energy in Euclidean space with Dirichlet boundary conditions for two planar models, namely: i. the non-relativistic Landau problem for a charged particle of mass m for which - irrespective of the sign of the charge - the energy is negative, and ii. the model of a real, massive, noninteracting relativistic scalar field theory in 2 + 1 dimensions, for which the Casimir energy density is non-negative and is expressed in terms of the Lerch transcendent xxx and the polylogarithm xxx with 0 < xxx < 1 and n = 2, 3.Comment: 5 pages, 2 figures,IMFP2009 conference,to appear in forthcoming AIP Conf.Proc.1150 Request:There are three mathematical symbols denoted by xxx in the abstract below which are otherwise present in the abstract of the submission.Could you please include them so that the abstract below is complet