Casimir effect and renormalization group

We discuss the Casimir energy (vacuum energy) for interaction theories, by means of renormalization (RG) methods. We find the RG improved vacuum energy for (i) QED between two plates, (ii) scalar electrodynamics in De Sitter space, and (iii) a charged scalar field in a constant electromagnetic field. The relevance of the interaction, taken into account via the RG improvement, is discussed for these examples. In particular, a numerical study of the improved vacuum energy in De Sitter space (effective cosmological constant) gives the range of parameters for which the energy tends to zero.