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.

arXiv comment19 pages

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