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 c in front of a plane. By regarding the Casimir energy as a functional of c , 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 c . 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.

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 non equidistant, 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. * mcrocce@df.uba.ar † dalvit@lanl.gov ‡ fmazzi@df.uba.ar

We consider a λφ 4 theory in Minkowski spacetime. We compute a "coarse grained effective action" by integrating out the field modes with 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 DeSitter spacetime. We show that the *

The Casimir force is the ultimate background in ongoing searches of extra-gravitational 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.Comment: 5 pages, 4 figure

The gravitational effect produced by a global monopole may be approximated by a solid deficit angle. As a consequence, the energy-momentum tensor of a quantum field will have a nonzero vacuum expectation value. Here we study this "vacuum-polarization effect" around the monopole. We find explicit expressions for both (d'),,,, and ( T,, ),,,, for a massless scalar field. The back reaction of the quantum field on the monopole metric is also investigated.

We study the primordial magnetic field generated by stochastic currents produced by scalar charged particles created at the beginning of the radiation dominated epoch. We find that for the mass range 10^(-6)GeV \leq m \leq 10^2 GeV, a field of sufficient intensity to seed different mechanisms of galactic magnetic field generation, while still consistent with observational and theoretical constraints, is created coherently over a galactic scale.Comment: accepted for publication in Phys. Rev.

We compute the photon creation inside a perfectly conducting, three dimensional oscillating cavity, taking the polarization of the electromagnetic field into account. As the boundary conditions for this field are both of Dirichlet and (generalized) Neumann type, we analyze as a preliminary step the dynamical Casimir effect for a scalar field satisfying generalized Neumann boundary conditions. We show that particle production is enhanced with respect to the case of Dirichlet boundary conditions. Then we consider the transverse electric and transverse magnetic polarizations of the electromagnetic field. For resonant frequencies, the total number of photons grows exponentially in time for both polarizations, the rate being greater for transverse magnetic modes.

We calculate the exact Casimir interaction energy between two perfectly conducting, very long, eccentric cylindrical shells using a mode summation technique. Several limiting cases of the exact formula for the Casimir energy corresponding to this configuration are studied both analytically and numerically. These include concentric cylinders, cylinder-plane, and eccentric cylinders, for small and large separations between the surfaces. For small separations we recover the proximity approximation, while for large separations we find a weak logarithmic decay of the Casimir interaction energy, typical of cylindrical geometries.