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 φ4 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.
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