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This chapter contains conclusions and some words about the outlook. The main conclusion is that at present there is already very good agreement between the theory, adapted for the case of real boundaries, and the measurements of the Casimir force. The generalization of this theory to the case of materials with spatial dispersion and a more fundamental approach to the Casimir effect at nonzero temperature are expected in the near future. The applications of the Casimir effect in both fundamental physics and nanotechnology appear very promising and may have an unexpected impact on basic scientific concepts and technological approaches.

This chapter opens the part of the book devoted to quantum vacuum in non-trivial gravitational background and to vacuum energy. There are several macroscopic phenomena, which can be directly related to the properties of the physical quantum vacuum. The Casimir effect is probably the most accessible effect of the quantum vacuum. The chapter discusses different types of Casimir effect in condensed matter in restricted geometry, including the mesoscopic Casimir effect and the dynamic Casimir effect resulting in the force acting on a moving interface between ³He-A and ³He-B, which serves as a perfect mirror for the ‘relativistic’ quasiparticles living in ³He-A. It also discusses the vacuum energy and the problem of cosmological constant. Giving the example of quantum liquids it is demonstrated that the perfect vacuum in equilibrium has zero energy, while the nonzero vacuum energy arises due to perturbation of the vacuum state by matter, by texture, which plays the role of curvature, by boundaries due to the Casimir effect, and by other factors. The magnitude of the cosmological constant is small, because the present universe is old and the quantum vacuum is very close to equilibrium. The chapter discusses why our universe is flat, why the energies of the true vacuum and false vacuum are both zero, and why the perfect vacuum (true or false) is not gravitating.

During his first decade at the University of California at Los Angeles (UCLA), Julian Schwinger was actively engaged in recasting high-energy physics into his own language, be it through unconventional interpretations of the psi particles, non-speculative approaches to deep inelastic scattering, or the field theory of magnetic charge. However, the reception to this work was not so favorable. He had already abandoned writing his multivolume Particles, sources, and fields in 1974, precisely at the point where he was to begin dealing with strong and weak interactions. His last deep inelastic scattering paper was submitted in January 1977, while his sole foray into supersymmetry was submitted in September 1978. His final publication on synchrotron radiation appeared in 1978. So it may be fair to say that the hostility toward source theory pushed him out of the mainstream, and into projects where his still formidable strengths could make an impact. There are four well-defined themes that occupied the final two decades of his life: the Casimir effect and Schwinger's attempt to explain it in terms of source theory, the statistical (or Thomas-Fermi) atom, cold fusion, and sonoluminescence.

This chapter begins with a normal-mode analysis of the classical electromagnetic field in an ideal cavity. The resulting expression for the electromagnetic energy has the same form as the energy of a collection of harmonic oscillators, called radiation oscillators. This analogy is the basis for a quantization conjecture in which the classical mode amplitudes are replaced by photon creation and annihilation operators, obeying a version of the canonical commutation relations of quantum mechanics. Fock space is constructed by repeated application of creation operators to the vacuum state. Pure and mixed quantum states of light are described, respectively, by Fock-space vectors satisfying the Schrödinger equation, and density operators satisfying the quantum Liouville equation. The notions of normal ordering and vacuum fluctuations are introduced, and the latter is used to explain the Casimir effect.

This chapter explores electromagnetic-matter interactions from photon to extinction length scales, i.e., nanometer of X-ray and above. Starting with Casimir-Polder effect to understand interactions of metals and dielectrics at near-atomic distance scale, it stretches to larger wavelengths to explore optomechanics and its ability for energy exchange and signal transduction between PHz and GHz. This range is explored with near-quantum sensitivity limits. The chapter also develops the understanding phononic bandgaps, and for photons, it explores the use of energetic coupling for useful devices such as optical tweezers, confocal microscopes and atomic clocks. It also explores miniature accelerators as a frontier area in accelerator physics. Plasmonics—the electromagnetic interaction with electron charge cloud—is explored for propagating and confined conditions together with the approaches’ possible uses. Optoelectronic energy conversion is analyzed in organic and inorganic systems, with their underlying interaction physics through solar cells and its thermodynamic limit, and quantum cascade lasers.

In this chapter, the path integral approach is extended from quantum mechanics to the simplest field theory containing a single real scalar field. First the generating functionals of (dis-) connected n-point Green functions are introduced, then the Feynman propagator of the scalar field is derived and causality is discussed. The exchange of a space-like scalar particle between two static sources is examined and it is shown that it leads to an attractive Yukawa potential. The Casimir effect is used to demonstrate that vacuum fluctuations have physical consequences.