Casimir Effect of Strongly Interacting Scalar Fields

Non-trivial $\phi ^{4}$-theory is studied in a renormalisation group invariant approach inside a box consisting of rectangular plates and where the scalar modes satisfy periodic boundary conditions at the plates. It is found that the Casimir energy exponentially approaches the infinite volume limit, the decay rate given by the scalar condensate. It therefore essentially differs from the power law of a free theory. This might provide experimental access to properties of the non-trivial vacuum. At small interplate distances 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 are presented.