Local zeta regularization and the Casimir effect

Details Local zeta regularization and the Casimir effect Local zeta regularization and the Casimir effect

2011-04-21

arxiv.org/abs/1104.4330v2

Prog. Theor. Phys. 126(3) (2011), 419-434

Physics

Mathematical Physics

It differs from the previous arXiv version v1 only for misprint corrections. An enlarged version has been published in Progres

Scientific paper

10.1143/PTP.126.419

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.

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