On the numerical technique of Casimir energy calculation

TL;DR

This paper introduces a new numerical method for calculating Casimir energy that efficiently handles logarithmic divergences and is applicable even when energy levels are only numerically accessible.

Contribution

A novel non-subtractive renormalization technique for Casimir energy that works with purely numerical spectral data and divergent terms.

Findings

Method successfully handles logarithmic divergences.

Numerical results agree with traditional subtraction methods.

Applicable when spectral equations are not analytically solvable.

Abstract

A non-subtractive recipe of Casimir energy renormalization efficient in the presence of logarithmically divergent terms is proposed. It is demonstrated that it can be applied even in such cases, when energy levels can be obtained only numerically whereas neither their asymptotical behavior, nor the analytical form of the corresponding spectral equation can be studied. The results of numerical calculations performed with this method are compared to those obtained by means of explicit subtraction of divergent terms from energy.