The Mechanical Response of Vacuum

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-wavevector 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.