The effects induced by the quantum vacuum fluctuations of one massless real scalar field on a configuration of two partially transparent plates are investigated. The physical properties of the infinitely thin plates are simulated by means of Dirac-$\delta -{\delta }^{\prime }$ point interactions. It is shown that the distortion caused on the fluctuations by this external background gives rise to a generalization of Robin boundary conditions. The $T$ operator for potentials concentrated on points with nondefined parity is evaluated with total generality. The quantum vacuum interaction energy between the two plates is computed in several dimensions using the $TGTG$ formula to find positive, negative, and zero Casimir energies. The parity properties of the $\delta -{\delta }^{\prime }$ potential demands that one distinguish between opposite and identical objects. It is shown that between identical sets of $\delta -{\delta }^{\prime }$ plates, repulsive, attractive, or null quantum vacuum forces arise. However, there is always attraction between a pair of opposite $\delta -{\delta }^{\prime }$ plates.

• Received 15 July 2014

DOI:https://doi.org/10.1103/PhysRevD.91.025028