Vacuum energy for a scalar field with self-interaction in (1+1) dimensions

Abstract

We calculate the vacuum (Casimir) energy for a scalar field with ${\varphi }^4$ self-interaction in (1+1) dimensions non perturbatively, i.e., in all orders of the self-interaction. We consider massive and massless fields in a finite box with Dirichlet boundary conditions and on the whole axis as well. For strong coupling, the vacuum energy is negative indicating some instability.

19 pages

References in corpus (1)

• The closed piecewise uniform string revisited