The Casimir effect: Recent controversies and progress

Abstract

The phenomena implied by the existence of quantum vacuum fluctuations, grouped under the title of the Casimir effect, are reviewed, with emphasis on new results discovered in the past four years. The Casimir force between parallel plates is rederived as the strong-coupling limit of $\delta$-function potential planes. The role of surface divergences is clarified. A summary of effects relevant to measurements of the Casimir force between real materials is given, starting from a geometrical optics derivation of the Lifshitz formula, and including a rederivation of the Casimir-Polder forces. A great deal of attention is given to the recent controversy concerning temperature corrections to the Casimir force between real metal surfaces. A summary of new improvements to the proximity force approximation is given, followed by a synopsis of the current experimental situation. New results on Casimir self-stress are reported, again based on $\delta$- function potentials. Progress in understanding divergences in the self-stress of dielectric bodies is described, in particular the status of a continuing calculation of the self-stress of a dielectric cylinder. Casimir effects for solitons, and the status of the so-called dynamical Casimir effect, are summarized. The possibilities of understanding dark energy, strongly constrained by both cosmological and terrestrial experiments, in terms of quantum fluctuations are discussed. Throughout, the centrality of quantum vacuum energy in fundamental physics in emphasized.

80 pages, 7 eps figures, uses iopart.cls and iopams.sty

References in corpus (19)

• Gauge Theories with Cayley-Klein $SO(2;j)$ and $SO(3;j)$ Gauge Groups
• Casimir-Polder interaction between an atom and a cavity wall under the influence of real conditions
• The Casimir force between rough metallic plates
• The history of the cosmological constant problem
• New Challenges and Directions in Casimir Force Experiments
• Casimir effect between dissimilar materials: a test for the proximity theorem
• Dispersive force between dissimilar materials: geometrical effects
• Worldline Approach To The Casimir Effect
• Electromagnetic vacuum fluctuations, Casimir and Van der Waals forces
• Temperature Dependence of the Casimir Force for Metals
• Viscous Cosmology, Entropy, and the Cardy-Verlinde Formula
• The Casimir force between real mirrors at non zero temperature
• The Low-Frequency Character of the Thermal Correction to the Casimir Force between Metallic Films
• Geometry Dependence of Casimir Forces beyond the Proximity Approximation
• Comment on "Does the transverse electric zero mode contribute to the Casimir effect for a metal?"
• Generalized Bogoliubov Transformation, Fermion Field and Casimir Effect in a Box
• Properties of metallic films in precise calculation of the Casimir force
• Casimir force between a sphere and a plane: spectral representation formalism
• New developments in the quantization of supersymmetric solitons (kinks, vortices and monopoles)

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