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

TL;DR

This paper computes the non-perturbative vacuum energy of a self-interacting scalar field in (1+1) dimensions, revealing negative energies at strong coupling which suggest potential instabilities.

Contribution

It provides a non-perturbative calculation of the vacuum energy for a self-interacting scalar field in (1+1) dimensions, including massive and massless cases, with various boundary conditions.

Findings

Vacuum energy is negative at strong coupling.

Results apply to both finite and infinite domains.

Non-perturbative approach extends previous perturbative studies.

Abstract

We calculate the vacuum (Casimir) energy for a scalar field with $\phi^4$ 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.