Some recent results in calculation of the Casimir energy at zero and finite temperature

TL;DR

This paper reviews recent advances in calculating Casimir energy at zero and finite temperatures, focusing on material effects, spectral geometry methods, and high-temperature behavior analysis.

Contribution

It introduces new approaches for incorporating material properties, applying spectral geometry techniques, and deriving high-temperature Casimir energy formulas.

Findings

Material characteristics significantly influence vacuum energy.

Spectral geometry methods provide insight into divergence origins.

Universal high-temperature Casimir energy formula developed.

Abstract

The survey summarizes briefly the results obtained recently in the Casimir effect studies considering the following subjects: i) account of the material characteristics of the media and their influence on the vacuum energy (for example, 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) universal method for calculating the high temperature dependence of the Casimir energy in terms of heat kernel coefficients.