Multiple Scattering Methods in Casimir Calculations

Abstract

Multiple scattering formulations have been employed for more than 30 years as a method of studying the quantum vacuum or Casimir interactions between distinct bodies. Here we review the method in the simple context of $\delta$-function potentials, so-called semitransparent bodies. (In the limit of strong coupling, a semitransparent boundary becomes a Dirichlet one.) After applying the method to rederive the Casimir force between two semitransparent plates and the Casimir self-stress on a semitransparent sphere, we obtain expressions for the Casimir energies between disjoint parallel semitransparent cylinders and between disjoint semitransparent spheres. Simplifications occur for weak and strong coupling. In particular, after performing a power series expansion in the ratio of the radii of the objects to the separation between them, we are able to sum the weak-coupling expansions exactly to obtain explicit closed forms for the Casimir interaction energy. The same can be done for the interaction of a weak-coupling sphere or cylinder with a Dirichlet plane. We show that the proximity force approximation (PFA), which becomes the proximity force theorem when the objects are almost touching, is very poor for finite separations.

21 pages, 7 figures, ReVTEX. Introduction shortened, Appendix A expanded, references added

References in corpus (28)

• The Casimir effect: Recent controversies and progress
• Casimir forces between arbitrary compact objects
• The Casimir effect within scattering theory
• Casimir interaction between a plate and a cylinder
• Casimir Effect on the Worldline
• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Casimir effect for curved geometries: PFA validity limits
• Scalar Casimir effect between Dirichlet spheres or a plate and a sphere
• Worldline algorithms for Casimir configurations
• Casimir effect with rough metallic mirrors
• Casimir Forces between Compact Objects: I. The Scalar Case
• Lateral Casimir force beyond the Proximity Force Approximation
• Casimir edge effects
• Exact Casimir interaction between eccentric cylinders
• Roughness correction to the Casimir force : Beyond the Proximity Force Approximation
• Geometry and Spectrum of Casimir Forces
• Exact zero-point interaction energy between cylinders
• Casimir Energies and Pressures for $\delta$-function Potentials
• Casimir Forces: An Exact Approach for Periodically Deformed Objects
• The lateral Casimir force beyond the proximity force approximation: a nontrivial interplay between geometry and quantum vacuum
• Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation
• Semiclassical analysis of Wigner $3j$-symbol
• How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy
• Exact Casimir Interaction Between Semitransparent Spheres and Cylinders
• The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell
• Casimir interaction between normal or superfluid grains in the Fermi sea
• Quantization of Hyperbolic N-Sphere Scattering Systems in Three Dimensions
• Local Casimir Energies for a Thin Spherical Shell

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• On the Casimir effect from the zero-point energy: A tangential force and its properties
• The proximity force approximation for the Casimir energy of plate-sphere and sphere-sphere systems in the presence of one extra compactified universal dimension
• Lateral Casimir forces on parallel plates and concentric cylinders with corugations
• Massive scalar Casimir interaction beyond proximity force approximation