Local zeta regularization and the Casimir effect

TL;DR

This paper pedagogically demonstrates how local zeta regularization can be used to compute the stress-energy tensor in the Casimir effect for a scalar field, providing a finite, direct method that aligns with traditional results.

Contribution

It introduces and exemplifies the local zeta regularization method for Casimir effect calculations, highlighting its advantages over traditional regularization techniques.

Findings

Local zeta regularization yields finite stress-energy tensor results.

Results agree with those obtained by point splitting regularization.

Method simplifies calculations by avoiding divergence subtraction.

Abstract

In this paper, whose aims are mainly pedagogical, we illustrate how to use the local zeta regularization to compute the stress-energy tensor of the Casimir effect. Our attention is devoted to the case of a neutral, massless scalar field in flat space-time, on a space domain with suitable (e.g., Dirichlet) boundary conditions. After a simple outline of the local zeta method, we exemplify it in the typical case of a field between two parallel plates, or outside them. The results are shown to agree with the ones obtained by more popular methods, such as point splitting regularization. In comparison with these alternative methods, local zeta regularization has the advantage to give directly finite results via analitic continuation, with no need to remove or subtract divergent quantities.