Casimir energies with finite-width mirrors

Abstract

We use a functional approach to the Casimir effect in order to evaluate the exact vacuum energy for a real scalar field in $d+1$ dimensions, in the presence of backgrounds that, in a particular limit, impose Dirichlet boundary conditions on one or two parallel surfaces. Outside of that limit, the background may be thought of as describing finite-width mirrors with frequency-dependent transmission and reflection coefficients. We provide new explicit results for the Casimir energy in some particular backgrounds

18 pages, no figures. Version to appear in Phys. Rev. D

References in corpus (21)

• New Developments in the Casimir Effect
• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Measurement of the Casimir force between parallel metallic surfaces
• Nonlinear Micromechanical Casimir Oscillator
• The Casimir effect: Recent controversies and progress
• Improved Precision Measurement of the Casimir Force Using Gold Surfaces
• Precise comparison of theory and new experiment for the Casimir force leads to stronger constraints on thermal quantum effects and long-range interactions
• Measurement of the Casimir force between dissimilar metals
• Template-stripped gold surfaces with 0.4 nm rms roughness suitable for force measurements. Application to the Casimir force in the 20-100 nm range
• Constraining New Forces in the Casimir Regime Using the Isoelectronic Technique
• Path Integral Approach to the Dynamic Casimir Effect with Fluctuating Boundaries
• The Dirichlet Casimir Problem
• Effect of hydrogen-switchable mirrors on the Casimir force
• The Casimir force and the quantum theory of lossy optical cavities
• On the Temperature Dependence of the Casimir Effect
• Thermal corrections to the Casimir effect
• Casimir Effect: The Classical Limit
• Comment on "On the temperature dependence of the Casimir effect"
• Quantum dissipative effects in moving mirrors: a functional approach
• Local and Global Casimir Energies for a Semitransparent Cylindrical Shell
• On the interaction of a charge with a thin plasma sheet

Cited by in corpus (11)

• Quantum field theory on toroidal topology: algebraic structure and applications
• Electromagnetic $\delta$-function sphere
• Casimir effect with dynamical matter on thin mirrors
• Neumann Casimir effect: a singular boundary-interaction approach
• Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $\delta$-potentials
• Lifshitz formula for the Casimir force and the Gelfand-Yaglom theorem
• Casimir effect with nonlocal boundary interactions
• Comment on "Casimir energies with finite-width mirrors"
• A Dual Path Integral Representation for Finite Temperature Quantum Field Theory
• Casimir type effects for scalar fields interacting with material slabs
• On the Casimir energy for scalar fields with bulk inhomogeneities