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

R. Guérout, A. Lambrecht, K. A. Milton, S. Reynaud

Published 2014-04-30, updated 2014-09-26Version 3

We carefully re-examine the conditions of validity for the consistent derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors. We recover the usual expression for the lossy Drude model, but not for the lossless plasma model. We give an interpretation of this new result in terms of the modes associated with the Foucault currents which play a role in the limit of vanishing losses, in contrast to common expectations.