Casimir effect with non-local boundary conditions

TL;DR

This paper investigates the Casimir effect for a massive scalar field with non-local boundary conditions, revealing that vacuum forces can be repulsive and lead to stable equilibrium distances between plates.

Contribution

It provides the first analysis of the Wightman function and vacuum expectation values for non-local boundary conditions in this context.

Findings

Vacuum forces can be repulsive at intermediate distances.

Stable equilibrium interplate distances can be achieved.

Non-local boundary conditions influence the Casimir force behavior.

Abstract

Non-local boundary conditions have been considered in theoretical high-energy physics with emphasis on one-loop quantum cosmology, one-loop conformal anomalies, Bose-Einstein condensation models and spectral branes. In the present paper, for the first time in the literature, the Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field satisfying non-local boundary conditions on a single plate and on two parallel plates. The vacuum forces acting on the plates are evaluated. Interestingly, suitable choices of the kernel in the non-local boundary conditions lead to forces acting on the plates that can be repulsive for intermediate distances. It is then possible to obtain a locally stable equilibrium value of the interplate distance stabilized by the vacuum forces.