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We carefully re-examine the conditions of validity for the consistentderivation of the Lifshitz-Matsubara sum formula for the Casimir pressurebetween metallic plane mirrors. We recover the usual expression for the lossyDrude model, but not for the lossless plasma model. We give an interpretationof this new result in terms of the modes associated with the Foucault currentswhich play a role in the limit of vanishing losses, in contrast to commonexpectations.

Derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors