$\delta-\delta^\prime$ generalized Robin boundary conditions and quantum vacuum fluctuations

TL;DR

This paper explores how quantum vacuum fluctuations affect two partially transparent plates modeled by delta-delta' interactions, leading to a generalized Robin boundary condition and revealing conditions for repulsive Casimir forces.

Contribution

It introduces a generalized Robin boundary condition arising from delta-delta' interactions and computes the quantum vacuum interaction energy for these configurations.

Findings

Generalized Robin boundary conditions from delta-delta' interactions.

Calculation of Casimir energies including repulsive cases.

Explicit T-operator for non-parity symmetric potentials.

Abstract

The effects induced by the quantum vacuum fluctuations of one massless real scalar field on a configuration of two partially transparent plates are investigated. The physical properties of the infinitely thin plates are simulated by means of Dirac-$\delta-\delta^\prime$ point interactions. It is shown that the distortion caused on the fluctuations by this external background gives rise to a generalization of Robin boundary conditions. The $T$-operator for potentials concentrated on points with non defined parity is computed with total generality. The quantum vacuum interaction energy between the two plates is computed using the $TGTG$ formula to find positive, negative, and zero Casimir energies. The parity properties of the $\delta-\delta^\prime$ potential allow repulsive quantum vacuum force between identical plates.