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

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

Wave propagation and group velocity

Strong-field effects in laboratory and astrophysical plasmas and high intensity laser and cavity systems are considered, related to quantum electrodynamical (QED) photon-photon scattering. Current state-of-the-art laser facilities are close to reaching energy scales at which laboratory astrophysics will become possible. In such high energy density laboratory astrophysical systems, quantum electrodynamics will play a crucial role in the dynamics of plasmas and indeed the vacuum itself. Developments such as the free-electron laser may also give a means for exploring remote violent events such as supernovae in a laboratory environment. At the same time, superconducting cavities have steadily increased their quality factors, and quantum nondemolition measurements are capable of retrieving information from systems consisting of a few photons. Thus, not only will QED effects such as elastic photon-photon scattering be important in laboratory experiments, it may also be directly measurable in cavity experiments. Here implications of collective interactions between photons and photon-plasma systems are described. An overview of strong field vacuum effects is given, as formulated through the Heisenberg-Euler Lagrangian. Based on the dispersion relation for a single test photon traveling in a slowly varying background electromagnetic field, a set of equations describing the nonlinear propagation of an electromagnetic pulse on a radiation plasma is derived. The stability of the governing equations is discussed, and it is shown using numerical methods that electromagnetic pulses may collapse and split into pulse trains, as well as be trapped in a relativistic electron hole. Effects, such as the generation of novel electromagnetic modes, introduced by QED in pair plasmas is described. Applications to laser-plasma systems and astrophysical environments are also discussed.

Nonlinear collective effects in photon-photon and photon-plasma interactions

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

We review the literature on possible violations of the superposition principle for electromagnetic fields in vacuum from the earliest studies until the emergence of renormalized QED at the end of the 1940's. The exposition covers experimental work on photon-photon scattering and the propagation of light in external electromagnetic fields and relevant theoretical work on nonlinear electrodynamic theories (Born-Infeld theory and QED) until the year 1949. To enrich the picture, pieces of reminiscences from a number of (theoretical) physicists on their work in this field are collected and included or appended.

pdf/photon-photon-scattering-and-related-phenomena-experimental-4fivhl0c4n.pdf

Photon-photon scattering and related phenomena. Experimental and theoretical approaches: The early period

http://inspirehep.net/record/846024/files/arXiv:1002.2737.pdf

Nonlinear Bogolyubov-Valatin transformations: Two modes

Based on a methodological analysis of the effective action approach certain conceptual foundations of quantum field theory are reconsidered to establish a quest for an equation for the effective action. Relying on the functional integral formulation of Lagrangian quantum field theory a functional integral equation for the complete effective action is proposed which can be understood as a certain fixed point condition. This is motivated by a critical attitude towards the distinction artificial from an experimental point of view between classical and effective action. While for free field theories nothing new is accomplished, for interacting theories the concept differs from the established paradigm. The analysis of this new concept is concentrated on gauge field theories treating QED as the prototype model. An approximative approach to the functional integral equation for the complete effective action of QED is exploited to obtain certain nonperturbative information about the quadratic kernels of the action. As particular application the approximative calculation of the QED coupling constant $\alpha$ is explicitly studied. It is understood as one of the characteristics of a fixed point given as a solution of the functional integral equation proposed. Finally, within the present approach the vacuum energy problem is considered and possible implications on the induced gravity concept are contemplated.

A Functional Integral Equation for the Complete Effective Action in Quantum Field Theory

The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model

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