Local zeta regularization and the Casimir effect
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.
Keywords
Cite
@article{arxiv.1104.4330,
title = {Local zeta regularization and the Casimir effect},
author = {Davide Fermi and Livio Pizzocchero},
journal= {arXiv preprint arXiv:1104.4330},
year = {2011}
}
Comments
It differs from the previous arXiv version v1 only for misprint corrections. An enlarged version has been published in Progress of Theoretical Physics