Scalar Casimir effect with non-local boundary conditions

TL;DR

This paper investigates the effects of non-local boundary conditions on a scalar field, revealing that such conditions can induce repulsive Casimir forces at certain distances, with implications for quantum field theory and related areas.

Contribution

It introduces a detailed analysis of the scalar Casimir effect under non-local boundary conditions, highlighting the possibility of repulsive forces due to specific kernel choices.

Findings

Non-local boundary conditions alter the Casimir force behavior.

Repulsive forces can occur at intermediate distances.

The study provides explicit calculations of the Wightman function and energy-momentum tensor.

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. We have therefore studied the Wightman function, the vacuum expectation value of the field square and the energy-momentum tensor for a massive scalar field satisfying non-local boundary conditions on a single and two parallel plates. Interestingly, we find that 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.