New Developments in the Casimir Effect

We provide a review of both new experimental and theoretical developments in the Casimir e ect. The Casimir e ect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus, the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the in3nities in the 3eld theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Di erent representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of con3gurations of interest to applications are calculated. We stress the development of the Casimir force for real media including e ects of nonzero temperature, 3nite conductivity of the boundary metal and surface roughness. Also, the combined e ect of these important factors is investigated in detail on the basis of condensed matter physics and quantum 3eld theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting 3rst with the older measurements and 3nishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements. c © 2001 Elsevier Science B.V. All rights reserved. PACS: 12.20.−m; 11.10.Wx; 72.15.−v; 68.35.Ct; 12.20.Fv; 14.80.−j