Casimir effect of strongly interacting scalar fields

The Casimir effect of nontrivial φ4 theory is studied for a rectangular box. The scalar modes satisfy periodic boundary conditions, which corresponds to a compactification of space. Nontrivial φ4 theory is obtained by an analytic continuation of the theory to negative quartic coupling. This theory is studied in a renormalization-group-invariant approach. It is found that the Casimir energy exponentially approaches the infinite volume limit, the decay rate given by the scalar condensate. This behavior is very different from the power law of a free theory. This might provide experimental access to properties of the nontrivial vacuum. At small compactification lengths the system can no longer tolerate a scalar condensate, and a first order phase transition to the perturbative phase occurs. The dependence of the vacuum energy density and the scalar condensate on the box dimensions is presented.