Non-superposition effects in the Dirichlet-Casimir effect

We study non-superposition effects in the Dirichlet-Casimir interaction energy for N boundaries in d spatial dimensions, quantifying its departure from the case of an interaction where a superposition principle is valid. We first derive some general results about those effects, and then show that they become negligible only when the distances between surfaces are larger than the sizes of each individual surface. We consider different examples of this situation in one, two and three spatial dimensions. Finally, we present two examples, corresponding to highly symmetric configurations involving more than two surfaces. We show that, even though superposition is not valid, the total interaction energy may nevertheless be expressed as a sum of (non-Casimir) energies involving pairs of surfaces.