When the Casimir energy is not a sum of zero-point energies

Details When the Casimir energy is not a sum of zero-point energies When the Casimir energy is not a sum of zero-point energies

2001-08-31

arxiv.org/abs/hep-th/0108240v2

Phys.Rev. D65 (2002) 045004

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, REVTEX, typos corrected, references added/updated

Scientific paper

We compute the leading radiative correction to the Casimir force between two parallel plates in the $\lambda\Phi^4$ theory. Dirichlet and periodic boundary conditions are considered. A heuristic approach, in which the Casimir energy is computed as the sum of one-loop corrected zero-point energies, is shown to yield incorrect results, but we show how to amend it. The technique is then used in the case of periodic boundary conditions to construct a perturbative expansion which is free of infrared singularities in the massless limit. In this case we also compute the next-to-leading order radiative correction, which turns out to be proportional to $\lambda^{3/2}$.

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