Wightman function and Casimir densities for Robin plates in the Fulling-Rindler vacuum

TL;DR

This paper analyzes the vacuum expectation values and Casimir forces for a scalar field between two uniformly accelerated plates with Robin boundary conditions in the Fulling-Rindler vacuum, revealing conditions for repulsive and attractive forces.

Contribution

It provides a detailed calculation of the Wightman function and Casimir densities for Robin plates in accelerated motion, including new insights into the force behavior based on boundary parameters.

Findings

Interaction forces can be repulsive or attractive depending on parameters.

Explicit expressions for vacuum densities are derived using Abel-Plana formula.

Limiting cases and force behaviors are thoroughly analyzed.

Abstract

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the region between two infinite parallel plates moving by uniform proper acceleration. We assume that the field is prepared in the Fulling-Rindler vacuum state and satisfies Robin boundary conditions on the plates. The mode-summation method is used with a combination of a variant of the generalized Abel-Plana formula. This allows to extract manifestly the contributions to the expectation values due to a single boundary and to present the second plate-induced parts in terms of exponentially convergent integrals. Various limiting cases are investigated. The vacuum forces acting on the boundaries are presented as a sum of the self-action and 'interaction' terms. The first one contains well known surface divergences and needs a further renormalization. The 'interaction' forces between the plates are investigated as functions of the proper accelerations and coefficients in the boundary conditions. We show that there is a region in the space of these parameters in which the 'interaction' forces are repulsive for small distances and attractive for large distances.