New vacuum boundary effects of massive field theories

Analytical arguments suggest that the Casimir energy in 2+1 dimensions for gauge theories decays exponentially with the distance between the boundaries. The phenomenon has also been observed by non-perturbative numerical simulations. The dependence of this exponential decay on the different boundary conditions could help into a better understanding of the infrared behavior of these theories and in particular their mass spectrum. A similar phenomenon is expected to hold in 3+1 dimensions. Motivated by this feature we analyze the dependence of the exponential decay of Casimir energy for different boundary conditions of massive scalar fields in 3+1 dimensional spacetimes. We show that boundary conditions can be classified in two different families according to the rate of exponential decay of the Casimir energy. If the boundary conditions on each boundary are independent (e.g. both boundaries satisfy Dirichlet boundary conditions), the Casimir energy is exponentially decaying two times faster than when the boundary conditions interconnect the two boundary plates (e.g. for periodic or antiperiodic boundary conditions). These results will be useful for a comparison with the Casimir energy in the non-perturbative regime of non-Abelian gauge theories.