Calculation of the Casimir energy at zero and finite temperature: Some recent results

Abstract

This survey summarizes briefly results obtained recently in the Casimir energy studies devoted to the following subjects: i) account of the material characteristics of the media in calculations of the vacuum energy (for example, Casimir energy of a dilute dielectric ball); ii) application of the spectral geometry methods for investigating the vacuum energy of quantized fields with the goal to gain some insight, specifically, in the geometrical origin of the divergences that enter the vacuum energy and to develop the relevant renormalization procedure; iii) a universal method for calculating the high temperature dependence of the Casimir energy in terms of heat kernel coefficients. A special attention is payed to the mathematical tools applied in this field, namely, to the spectral zeta function method and heat kernel technique.

arXiv comment75 pages, 1 figure (eps file), 1 table, RevTeX; v2: some changes and additions as well as new references are introduced, the version to be published in Rivista del Nuovo Cimento