2008/01/31 by C. D. Fosco, Fernando C. Lombardo, F. C. Lombardo +2
Mathematics · Physics and Astronomy · #Action (physics) #Boundary (topology) #Boundary value problem #Casimir effect #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Dirichlet boundary condition #Geometry #Limit (mathematics) #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Reflection (computer programming) #Scalar (mathematics) #Scalar field #Theoretical physics #Vacuum energy #hep-ph #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.77.085018
published as Phys.Rev.D77:085018,2008 · 18 pages, no figures. Version to appear in Phys. Rev. D
arxiv created 2008/03/13 · openalex publication_date 2008/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 backgrounds are described by a nonlocal effective action and may be thought of as modelling finite-width mirrors with frequency-dependent transmission and reflection coefficients. We obtain formal expressions for the Casimir energy in general backgrounds, and provide new explicit results in some particular cases.