We consider a λ${\mathrm{\phi }}^4$ theory in Minkowski spacetime. We compute a ‘‘coarse-grained effective action’’ by integrating out the field modes with a wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients of this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. © 1996 The American Physical Society.

The proximity force approximation (PFA) has been widely used as a tool to evaluate the Casimir force between smooth objects at small distances. In spite of being intuitively easy to grasp, it is generally believed to be an uncontrolled approximation. Indeed, its validity has only been tested in particular examples, by confronting its predictions with the next-to-leading-order (NTLO) correction extracted from numerical or analytical solutions obtained without using the PFA. In this article we show that the PFA and its NTLO correction may be derived within a single framework, as the first two terms in a derivative expansion. To that effect, we consider the Casimir energy for a vacuum scalar field with Dirichlet conditions on a smooth curved surface described by a function $\psi${} in front of a plane. By regarding the Casimir energy as a functional of $\psi${}, we show that the PFA is the leading term in a derivative expansion of this functional. We also obtain the general form of the corresponding NTLO correction, which involves two derivatives of $\psi${}. We show, by evaluating this correction term for particular geometries, that it properly reproduces the known corrections to PFA obtained from exact evaluations of the energy.

A primordial magnetic field may be generated during an inflationary period if conformal invariance is broken. We reexamine and generalize previous results about the magnetic field produced by couplings of the form ${\mathit{R}}^{\mathit{n}}$ ${\mathit{F}}_{\mathrm{\mu }\nu }$ ${\mathit{F}}^{\mathrm{\mu }\nu }$. We show that the amplitude of the magnitude field depends strongly on n. For adequate values of n the field produced can serve as a seed for galactic magnetic fields. We also compute the effective interaction between the electromagnetic field and the geometry in the context of scalar QED (with and without classical conformal invariance). In both cases, the ampliutde of the magnetic field is too small to be of astrophysical interest. © 1995 The American Physical Society.

We analyze the problem of photon creation inside a perfectly conducting, rectangular, three-dimensional cavity with one oscillating wall. For some particular values of the frequency of the oscillations the system is resonant. We solve the field equation using multiple scale analysis and show that the total number of photons inside the cavity grows exponentially in time. This is also the case for slightly off-resonance situations. Although the spectrum of a cavity is in general nonequidistant, we show that the modes of the electromagnetic field can be coupled, and that the rate of photon creation strongly depends on this coupling. We also analyze the thermal enhancement of the photon creation.

The Casimir force is the ultimate background in ongoing searches for extragravitational forces in the micrometer range. Eccentric cylinders offer favorable experimental conditions for such measurements as spurious gravitational and electrostatic effects can be minimized. Here we report on the evaluation of the exact Casimir interaction between perfectly conducting eccentric cylinders using a mode summation technique, and study different limiting cases of relevance for Casimir force measurements, with potential implications for the understanding of mechanical properties of nanotubes.