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

Luiz C. de Albuquerque·R. M. Cavalcanti
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Abstract

We compute the leading radiative correction to the Casimir force between two parallel plates in the $λΦ^4$ 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 $λ^{3/2}$.

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Luiz C. de Albuquerque, R. M. Cavalcanti. 2002-01-16. When the Casimir energy is not a sum of zero-point energies. https://doi.org/10.1103/physrevd.65.045004

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