A path integral formulation is developed for the dynamic Casimir effect. It allows us to study arbitrary deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the intervening vacuum is calculated to linear order in the frequency--wave-vector plane. For a single corrugated plate we find a correction to mass at low frequencies, and an effective shear viscosity at high frequencies, both anisotropic. For two plates there is resonant dissipation for all frequencies greater than the lowest optical mode of the cavity.
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Golestanian et al. (1997) studied this question.
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