On the possibility of the implicit renormalization procedure for the Casimir energy

TL;DR

This paper introduces an implicit renormalization method for Casimir energy calculations that reduces ambiguity and improves computational efficiency, applicable to both analytically and numerically defined spectra.

Contribution

It presents a novel implicit renormalization procedure for Casimir energy that minimizes indeterminacy and enhances computational efficiency over traditional methods.

Findings

Reduces ambiguity in regularization choices

Applicable to systems with numerical spectra

More computationally efficient than standard methods

Abstract

We propose a procedure for the renormalization of Casimir energy, that is based on the implicit versions of standard steps of renormalization procedure --- regularization, subtraction and removing the regularization. The proposed procedure is based on the calculation of a set of convergent sums, which are related to the original divergent sum for the non-renormalized Casimir energy. Then one constructs a linear equations system, that connects this set of convergent sums with the renormalized Casimir energy, which is a solution to this equations system. This procedure slightly reduces the indeterminancy that arises in standard procedure when we choose the particular regularization and the explicit form of counterterm. The proposed procedure is more efficient from the computational point of view than the standard one. It can be applied not only for systems with the explicit transcendental equation for the spectrum, but also for systems with the spectrum that can be obtained only numerically.