1. Introduction I: PHYSICAL AND MATHEMATICAL FOUNDATIONS OF THE CASIMIR EFFECT FOR IDEAL BOUNDARIES 2. Simple models of the Casimir effect 3. Field quantization and vacuum energy in the presence of boundaries 4. Regularization and renormalization of the vacuum energy 5. The Casimir effect at nonzero temperature 6. Approximate and numerical approaches to the Casimir effect 7. The Casimir effect for two ideal metal planes 8. The Casimir effect in rectangular boxes 9. Single spherical and cylindrical boundaries 10. The Casimir force between objects of arbitrary shape 11. Spaces with non-Euclidean topology II: THE CASIMIR FORCE BETWEEN REAL BODIES 12. The Lifshitz theory of van der Waals and Casimir forces between plane dielectrics 13. The Casimir interaction between plates made of real metals at zero temperature 14. The Casimir interaction between real metals at nonzero temperature 15. The Casimir interaction between metal and dielectric 16. The Lifshitz theory of atom-wall interaction 17. The Casimir force between rough and corrugated surfaces III: MEASUREMENTS OF THE CASIMIR FORCE AND THEIR APPLICATIONS IN BOTH FUNDAMENTAL PHYSICS AND NANOTECHNOLOGY 18. General requirements for Casimir force measurements 19. Measurements of the Casimir force between equals 20. Measurements of the Casimir force with semiconductors 21. Measurements of the Casimir force in configurations with corrugated surfaces 22. Measurement of the Casimir-Polder force 23. Applications of the Casimir force in nanotechnology 24. Constraints on hypothetical interactions from the Casimir effect 25. Conclusions and outlook

Advances in the Casimir Effect

http://cds.cern.ch/record/503806/files/0106045.pdf

New developments in the Casimir effect

We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect 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 infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. 
The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing 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.

New Developments in the Casimir Effect

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the quantum-field-theory approach and evaluate the leading-order diagram in a theory with $2+1$-dimensional fermions interacting with $3+1$-dimensional photons. Next, we consider an effective theory for the electromagnetic field with matching conditions induced by quantum quasiparticles in graphene. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak. It exhibits a strong dependence on the mass of the quasiparticles in graphene.

Casimir interaction between a perfect conductor and graphene described by the Dirac model

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by rederiving the Lifshitz formula for infinite half-spaces, by demonstrating the Casimir-Polder to van der Waals crossover, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely, the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

Scattering theory approach to electrodynamic Casimir forces

Radiative corrections to the Casimir pressure under the influence of temperature and external fields

The framework of real time quantum field theory at finite temperature is generalized to include boundary conditions for the electromagnetic field strength tensor. In the perturbation theory the usual Feynman rules remain, only the photon propagator is modified. As a first application the Casimir effect is studied in the free field approximation and the known results are rederived with the new method.



Quantenfeldtheoretische Behandlung des Casimir-Effekts bei T > 0 (Realzeit-Formalismus — Free-Field-Approximation)



Der Formalismus der realzeitigen Quantenfeldtheorie bei endlicher Temperatur wird mit dem Ziel verallgemeinert, Randbedingungen fur den elektromagnetischen Feldstarketensor zu berucksichtigen. In der Storungstheorie bleiben die ublichen Feynman-Regeln ungeandert, lediglich der Photonpropagator wird modifiziert. Als eine erste Anwendung wird der Casimir-Effekt in der Free-Field-Approximation betrachtet, und die bekannten Resultate werden mit der neuen Methode abgeleitet.

Quantum Field Theoretic Treatment of the Casimir Effect at T > 0. Real Time Formalism - Free Field Approximation

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Radiative corrections to the Casimir pressure under the influence of temperature and external fields

Quantum Field Theoretic Treatment of the Casimir Effect at T > 0. Real Time Formalism - Free Field Approximation