Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $\delta$-potentials

Abstract

We calculate the Casimir energy for scalar fields in interaction with finite-width mirrors, described by nonlocal interaction terms. These terms, which include quantum effects due to the matter fields inside the mirrors, are approximated by means of a local expansion procedure. As a result of this expansion, an effective theory for the vacuum field emerges, which can be written in terms of generalized $\delta$-potentials. We compute explicitly the Casimir energy for these potentials and show that, for some particular cases, it is possible to reinterpret them as imposing imperfect Dirichlet boundary conditions

12 pages, two figures

References in corpus (12)

• New Developments in the Casimir Effect
• The Casimir effect: Recent controversies and progress
• Casimir Interactions for Anisotropic Magnetodielectric Metamaterials
• Exact results for Casimir forces using Surface Impedance: Nonlocal Media
• Multiple Scattering Methods in Casimir Calculations
• Casimir Energies and Pressures for $\delta$-function Potentials
• Spatial dispersion in Casimir forces: A brief review
• Casimir effect with dynamical matter on thin mirrors
• Casimir energies with finite-width mirrors
• Casimir effect with non-local boundary conditions
• Casimir effect with nonlocal boundary interactions
• Comment on "Casimir energies with finite-width mirrors"

Cited by in corpus (12)

• Quantum vacuum energies and Casimir forces between partially transparent $\delta$-function plates
• $\delta -{\delta }^{\prime }$ generalized Robin boundary conditions and quantum vacuum fluctuations
• Electromagnetic $\delta$-function sphere
• Neumann Casimir effect: a singular boundary-interaction approach
• Casimir force between $\delta -{\delta }^{\prime }$ mirrors transparent at high frequencies
• Temperature Dependence of the Effective Bag Constant and the Radius of a Nucleon in the Global Color Symmetry Model of QCD
• Inertial forces and dissipation on accelerated boundaries
• A Field Theoretic Approach to Roughness Corrections
• One-dimensional scattering of fermions in double Dirac delta potentials
• Vacuum fluctuations in the presence of nonlinear boundary conditions
• Quantum field theory at finite temperature for 3D periodic backgrounds
• Casimir energy through transfer operators for sine-Gordon backgrounds