Casimir Effect

The vacuum expectation values of the energy-momentum tensor are investigated for massless scalar fields satisfying Dicichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on two infinite parallel plates moving by uniform proper acceleration through the Fulling-Rindler vacuum. The scalar case is considered for general values of the curvature coupling parameter and in an arbitrary number of spacetime dimension. The mode-summation method is used with combination of a variant of the generalized Abel-Plana formula. This allows to extract manifestly the contributions to the expectation values due to a single boundary. The vacuum forces acting on the boundaries are presented as a sum of the self-action and interaction terms. The first one contains well known surface divergences and needs a further regularization. The interaction forces between the plates are always attractive for both scalar and electromagnetic cases. An application to the 'Rindler wall' is discussed.

Traditional studies of human consciousness assume the necessitation of dynamic, time-varying metabolic processes often without consideration of the properties of and interactions with the spatial environment within which these processes occur. Quantitative electroencephalographic (QEEG) measurements were obtained from an adult human brain specimen, preserved in ethanol-formalin-acetic acid (EFA). Probes were inserted into gyri approximating areas which underlie QEEG channels corresponding to the 10-20 International System of Electrode Placement and referenced to a living human ear. Before measurements were obtained, the specimen was submerged for 20 min in EFA (pH<3) or distilled H2O (pH > 5). During measurements, the brain was either placed on a flat surface, within a polystyrene box, or within a polyethylene human replica skull. Baseline measures were obtained with applied filters so as to eliminate ambient electromagnetic noise. Independent Component Analysis (ICA) performed upon the QEEG data revealed two major activation patterns. The first activation pattern consisted of a right temporo-occipital profile, which dominated all conditions. However, a second pattern emerged: bilateral frontal lobe and left supramarginal gyrus activation. This second pattern was only observed when the experimental conditions approximated those that would be expected to closely simulate the human body (i.e. brain pH approached neutrality and was contained within a skull). In order to identify a potential mechanism, environmental electrodynamics were considered. Raw data from all conditions as well as data collected from an induction coil which measures Schumann oscillations from the Earth’s geomagnetic field were extracted and spectral analyzed. Correlational analyses of spectral densities within the frequency band corresponding to the fundamental mode of the Schumann field (7Hz – 9Hz) revealed significant relationships that were present only when the brain was contained within a skull (r = -.25, p<.01) or approached pH neutrality (r = -.29, p< .001). These results are indicative of a
relationship between the Earth’s magnetic field, the human skull, water, and areas of the brain associated with the construction of the sense of self.

Over the last decade, there has been a respectable level of scientific interest regarding the concept of a warp drive. This is a hypothetical propulsion device that could theoretically circumvent the traditional limitations of special relativity which restricts spacecraft to sub-light velocities. Any breakthrough in this field would revolutionize space exploration and open the doorway to interstellar travel. This article discusses a novel approach to generating the warp bubble necessary for such propulsion; the mathematical details of this theory are discussed in an article published in the Journal of the British Interpanetary Society. The theory is based on some of the exciting predictions coming out of string theory and it is the aim of this article to introduce the warp drive idea from a non-mathematical perspective that should be accessible to a wide range of readers.

We discuss the Casimir effect for a massive bosonic field with mixed (Dirichlet-Neumann) boundary conditions. We use the ζ-function regularization prescription to obtain our physical results. Particularly, we analyse how the Casimir energy varies with the mass of the field and compare this mass dependence with those obtained for other boundary conditions. This is done graphically. Some other graphs involving a massive fermionic field are also included.

– Quantum fluctuations of the electromagnetic field in the medium surrounding two discharged macroscopic polarizable bodies induce a force between the two bodies, the so called Casimir force. In the last two decades many experiments have accurately measured this force, and significant efforts are made to harness it in the actuation of micro and nano machines. The inherent many body character of the Casimir force makes its computation very difficult in non-planar geometries, like the standard experimental sphere-plate configuration. Here we derive an approximate semi-analytic formula for the sphere-plate Casimir force, which is both easy to compute numerically and very accurate at all distances. By a comparison with the fully converged exact scattering formula, we show that the error made by the approximate formula is indeed much smaller than the uncertainty of present and foreseeable Casimir experiments.

An analysis of the physical implications of abstractness reveals the reality of three interconnected modes of existence: abstract, virtual and concrete. This triple-aspect monism clarifies the ontological status of subatomic quantum particles. It also provides a non-spooky solution to the weirdness of quantum physics and a new outlook for the mind-body problem. The ontological implications are profound for both physics and philosophy.

A framework for defining the physical basis of consciousness is derived in terms of the complementarity inherent in the cosmology of a continuous state conscious universe as it relates to self-organized living systems. The activity of a dynamic counterpart of standard static Casimir-like modes is described by an extended spacetime Cavity Quantum Electrodynamics in terms of a 12D Topological Field Theory that integrates gravity, electromagnetism and relativistic quantum field theory to develop the noetic action principle. Inherent self-organized teleological and intentional action on the spacetime geodesic cavities of the dynamic Casimir-like modes is mediated by a specific nonlocal unitary exchange quanta defined as the Noeon, that is indicative of an elan vital which also becomes associated with information and processing in the microtubule, synapse and other arenas of quantum brain dynamics where 'consciousness' couples to biological structure and biochemical species in terms of an elaborated definition of Eccles original philosophical concept of the Psychon. Novel ideas involving the cosmological Noumenon and brain Holoscape are presented including a basic mathematical formalism for the noetic action principle.

We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar and electromagnetic fields and calculate the limiting cases. For small separation we compare the exact results with the corresponding ones obtained in proximity force approximation. For the scalar field with Dirichlet boundary conditions, the low temperature correction is of order T 2 like for parallel planes. For the electromagnetic field it is of order T 4 . For high temperature we observe the usual picture that the leading order is given by the zeroth Matsubara frequency. The non-zero frequencies are exponentially suppressed except for the case of close separation. PACS numbers: 03.70.+k Theory of quantized fields 11.10.Wx Finite-temperature field theory 11.80.La Multiple scattering 12.20.Ds Specific calculations a [email protected] b [email protected]

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The living symphony of life sounds from deep within the microphysical, representing the veritable completion of the fabled Great Chain of Being. This sketch from 2015 can be coordinated with a much more concrete, recent description of the fundamental physical system of living motion and psychical reality at issue (especially the chirality that deeply informs musical thematics) now to be found in the author's 'Carlyle and the Idea' (2018) at Academia.Edu, toward which interested readers of this rough sketch are directed as a kind of paved road ahead.

In this work a generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermion counterpart of the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F.C. Khanna and A.E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on the thermofield dynamics approach. We analyze the energy-momentum tensor for the Casimir effect of a free massless fermion system in a N-dimensional box in contact with a heat bath. As a particular situation we calculate the Casimir energy and pressure for the field in a 3-dimensional box. One interesting result is that the attractive or repulsive nature of the Casimir pressure can change depending on the rate among the sizes. This fact is analyzed with specific examples.

PREFACE Gravitation (the attractive force existing between any two objects present in the universe that have mass) refers to one of the four fundamental forces in physics that are responsible for the attraction between masses. The other three fundamental forces are strong nuclear power, weak nuclear power and electromagnetism. In comparison to these other three forces, gravitation is certainly the "odd" one. While there is one single theory called the "Grand Unified Theory" that describes the other three forces, gravitation is explained solely by Einstein's general theory of relativity. According to that general theory of relativity, masses cause a distortion of the space-time structure around them. Any other mass that comes closer will experience the warping of space-time, and this appears to us as an attractive force between two masses. We will reason that this view is the wrong side of the coin. By turning over that same coin, another possibility appears that has a much stronger argument and brings out the true nature of gravitation. In that search, a number of fixed assumptions were reviewed and there, too, surprising new insights emerged. The phenomenon of the "spin" of elementary particles finally gets a plausible explanation, the reason for the expansion of the universe and the consequences involved showing a different reality, and the key in the lock of the Grand Unification theory has been turned, opening up a new dimension in physics. Let us take a first step : " … Einstein himself believed that the theory of general relativity could not properly function without a medium … " so the big question is where to look for that nebulous concept and determine what its energetic signature is?

The problem of estimating the thermal corrections to the Casimir and Casimir-Polder interactions in systems
involving conducting plates has attracted considerable attention in the recent literature on dispersion forces.
Alternative theoretical models, based on distinct low-frequency extrapolations of the plate’s reflection coefficient
for transverse electric
TE modes, provide widely different predictions for the magnitude of this correction.
In this paper we examine the most widely used prescriptions for this reflection coefficient from the point
of view of their consistency with the Bohr–van Leeuwen theorem of classical statistical physics, stating that at
thermal equilibrium transverse electromagnetic fields decouple from matter in the classical limit. We find that
the theorem is satisfied if and only if the TE reflection coefficient vanishes at zero frequency in the classical
limit. This criterion appears to rule out some of the models that have been considered recently for describing
the thermal correction to the Casimir pressure with nonmagnetic metallic plates.

The well known radiative correction is amplified by spin connection resonance, whereby the initially Coulombic potential in an easily ionized material is amplified to the point where electrons are released for use in circuits, energy production and energy savings. It is assumed that the radiative correction can be represented by an oscillating part of the fine structure constant. The methods of Einstein-Cartan-Evans (ECE) field theory are used to amplify the induced jitterbugging of the electron in each orbital that is the primary characteristic of the radiative correction. The latter is observed in well known phenomena such as the electron g factor, the Lamb shift and the Casimir effect. It is shown that the initially small radiative correction can be amplified for practical implementation.

The existence of irreducible field fluctuations in vacuum is an important prediction of quantum theory. These fluctuations have many observable consequences, like the Casimir effect which is now measured with good accuracy and agreement with theory, provided that the latter accounts for differences between real experiments and the ideal situation considered by Casimir. But the vacuum energy density calculated by adding field mode energies is much larger than the density observed around us through gravitational phenomena. This "vacuum catastrophe" is one of the unsolved problems at the interface between quantum theory on one hand, inertial and gravitational phenomena on the other hand. It is however possible to put properly formulated questions in the vicinity of this paradox. These questions are directly connected to observable effects bearing upon the principle of relativity of motion in quantum vacuum.

We study the modifications induced by spacetime anisotropy on the Casimir effect in the case of two parallel plates. Nonperturbative and perturbative regimes are analyzed. In the first case the Casimir force either vanishes or it reverses its direction which, in any case, makes the proposal untenable. On the other hand, the perturbative model enables us to incorporate appropriately the effects of spacetime anisotropy.

This is the Annual Progress Report of the theoretical particle theory group at the University of Florida under DOE Grant DEFG05-86ER40272. At present our group consists of four Full Professors (Field, Ramond, Thorn, Sikiuie), two Associate Professors (Qiu, Woodard), and one Assistant Professor (Kennedy). In addition, we have four postdoctoral research associ-ates and four graduate students. The research of our group covers a broad range of topics in theoretical high energy physics including both theory and phenomenology. Included in this report is a summary of the last several years, an outline of our current research program.

We present calculations of the quantum and thermal Casimir interaction between real mirrors in electromagnetic fields using the scattering approach. We begin with a pedagogical introduction of this approach in simple cases where the scattering is specular. We then discuss the more general case of stationary arbitrarily shaped mirrors and present in particular applications to two geometries of interest for experiments, that is corrugated plates and the plane-sphere geometry. The results nicely illustrate the rich correlations existing between material properties, temperature and geometry in the Casimir effect.

Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superposition of force components that are related to the electronic density-matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.

This review paper contains a concise introduction to highest weight representations of infinite dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in the paper is to be found in a very important feature of the theory of infinite dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated to new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function (therefore they are applicable, for instance, to topological Casimir effect calculations). We show that elliptic genera can be conveniently transformed into product expressions which can then inherit the homology properties of appropriate polygraded Lie algebras.

Using von Neumann’s continuous geometry in conjunction with A. Connes’ noncommutative geometry an exact mathematical-topological picture of quantum spacetime is developed ab initio. The final result coincides with the general conclusion of E-infinity theory and previous results obtained in the realm of high energy physics. In particular it is concluded that the quantum particle and the quantum wave spans quantum spacetime and conversely quantum particles and waves mutates from quantum spacetime.

In this study, influences of intermolecular forces on the dynamic pull-in instability of electrostatically actuated beams are investigated. The effects of midplane stretching, electrostatic actuation, fringing fields, and intermolecular forces are considered. The boundary conditions of the beams are clamped-free and clamped-clamped. A finite-element model is developed to discretize the governing equations, and Newmark time discretization is then employed to solve the discretized equations. The static pull-in instability is investigated to validate the model. Finally, dynamic pull-in instability of cantilevers and double-clamped beams are studied considering the Casimir and van der Waals effects. The results indicate that by increasing the Casimir and van der Waals effects, the effect of inertia on pull-in values considerably increases.

The Casimir stress on a spherical shell in de Sitter background for massless scalar field satisfying Dirichlet boundary conditions on the shell is calculated. The metric is written in conformally flat form. Although the metric is time dependent, no particles are created. The Casimir stress is calculated for inside and outside of the shell with different backgrounds corresponding to different cosmological constants. The detail dynamics of the bubble depends on different parameter of the model. Specifically, bubbles with true vacuum inside expands if the difference in the vacuum energies is small, otherwise it collapses. *

In recent years surface-light-scattering spectroscopy has been transformed from a complex optical experiment requiring substantial effort to operate effectively to a simpler instrument for which an accurate theory of operation has been developed. The accuracy and precision are sufficiently enhanced that refinement of the theory of spectral band shapes is justified to include more subtle effects such as bending moduli and thin-film forces associated with the van der Waals and the Casimir effects. We show how to develop extensions of the theory of interfacial fluctuations through the mass and the momentum balances of interfacial transport. We also show that free-energy functionals can be used to express curvature effects crisply. The results are detailed formulas that can be used to fit experimental spectra.

We extend our previous work [Phys. Rev. Lett. 100, 183602 (2008)] on the generalization of the Casimir-Lifshitz theory to treat anisotropic magnetodielectric media, focusing on the forces between metals and magnetodielectric metamaterials and on the possibility of inferring magnetic effects by measurements of these forces. We present results for metamaterials including structures with uniaxial and biaxial magnetodielectric anisotropies, as well as for structures with isolated metallic or dielectric properties that we describe in terms of filling factors and a Maxwell Garnett approximation. The elimination or reduction of Casimir "stiction" by appropriate engineering of metallic-based metamaterials, or the indirect detection of magnetic contributions, appear from the examples considered to be very challenging, as small background Drude contributions to the permittivity act to enhance attraction over repulsion, as does magnetic dissipation. In dielectric-based metamaterials the magnetic properties of polaritonic crystals, for instance, appear to be too weak for repulsion to overcome attraction. We also discuss Casimir-Polder experiments, that might provide another possibility for the detection of magnetic effects.

The purpose of this paper is to investigate the possibility that the Casimir effect, normally very weak, is strong enough to be significant on the scale of nuclear forces around 1 femtometer (fm = 10-15m). Computations were performed for the Casimir effect between two spheres using a proximity force approximation. It was found that at 2.6 fm the computed Casimir force is strong enough to overcome Coulomb repulsion and at 0.8 fm it is 20 times stronger than Coulomb repulsion. These values indicate that this strong Casimir force is important on scales of distance consistent with the nuclear force. With refinement it appears likely that the strong Casimir force can account for the nuclear force in its entirety allowing unification of the nuclear force with quantum electrodynamic theory.

The derivation of Casimir forces between dielectrics can be simplified by ignoring absorption, calculating energy changes due to displacements of the dielectrics, and only then admitting absorption by allowing permittivities to be complex. As a first step towards a better understanding of this situation we consider in this paper the model of a dielectric as a collection of oscillators, each of which is coupled to a reservoir giving rise to damping and Langevin forces on the oscillators and a noise polarization acting as a source of a fluctuating electromagnetic (EM) field in the dielectric. The model leads naturally to expressions for the quantized EM fields that are consistent with those obtained by different approaches, and also results in a fluctuation-dissipation relation between the noise polarization and the imaginary part of the permittivity. Our main result is the derivation of an expression for the QED energy density of a uniform dispersive, absorbing media in thermal equil...

Using the ray-optics approximation, we analyze the Casimir force in a two dimensional domain formed by two metallic blocks adjacent to parallel metallic sidewalls, which are separated from the blocks by a finite distance h. For h > 0, the ray-optics approach is not exact because diffraction effects are neglected. Nevertheless, we show that ray optics is able to qualitatively reproduce a surprising effect recently identified in an exact numerical calculation: the force between the blocks varies non-monotonically with h. In this sense, the ray-optics approach captures an essential part of the physics of multi-body interactions in this system, unlike simpler pairwise-interaction approximations such as PFA. Furthermore, by comparison to the exact numerical results, we are able to quantify the impact of diffraction on Casimir forces in this geometry.

Generalized uncertainty relations are known to provide a minimal length √ β. The effect of such minimal length in the Casimir-Polder interactions between neutral atoms is studied. The first order correction term in the minimal uncertainty parameter is derived and found to describe an attractive potential scaling as r −9 as opposed to the well known r −7 long range retarded potential.

In this article we investigate the Casimir effect in the presence of a medium by quantizing the Electromagnetic (EM) field in the presence of a magnetodielectric medium by using the path integral formalism. For a given medium with definite electric and magnetic susceptibilities, explicit expressions for the Casimir force are obtained which are in agree with the original Casimir force between two conducting parallel plates immersed in the quantum electromagnetic vacuum.

I discuss applications of the Bogoliubov transformations in the theory of photon creation from vacuum in cavities with moving walls (the nonstationary Casimir effect), their relations to the phenomenon of squeezing and some generalizations of these transformations to the case of coupled Fermi-Bose systems with quadratic Hamiltonians.

We consider the relations between the theory of quantum nonstationary damped oscillator and nonstationary Casimir effect in view of the problem of photon creation from vacuum inside the cavity with periodical time-dependent conductivity of a thin semiconductor boundary layer, which simulates periodical displacements of the cavity boundaries. We develop a consistent model of quantum damped harmonic oscillator with arbitrary time-dependent frequency and damping coefficients within the framework of Heisenberg-Langevin equations with two noncommuting delta-correlated noise operators. For the minimum noise set of correlation functions, whose time dependence follows that of the damping coefficient, we obtain the exact solution, which is a generalization of the Husimi solution for undamped nonstationary oscillator. It yields the general formula for the photon-generation rate under the resonance condition in the presence of dissipation. We obtain a simple approximate formula for a time-dependent shift of the complex resonance frequency. It depends only on the total energy of a short laser pulse (which creates an effective time-dependent electron-hole "plasma mirror" on the semiconductor-slab surface) and the recombination time. We show that damping due to a finite conductivity of the material significantly diminishes the photon-generation rate in the selected field mode of the cavity. Nonetheless, we have found optimum values of the parameters (laser pulse power, recombination time, and cavity dimensions), for which the effect of photon generation from vacuum could be observed in the experimental setup proposed in the University of Padua. We also provide with a list of publications from 2001 to 2005 devoted to the study on quantum-field interactions with moving boundaries (mirrors).

We review the relation between Casimir effect and geometry, emphasizing deviations from the commonly used Proximity Force Approximation (PFA). We use to this aim the scattering formalism which is nowadays the best tool available for accurate and reliable theory-experiment comparisons. We first recall the main lines of this formalism when the mirrors can be considered to obey specular reflection. We then discuss the more general case where non planar mirrors give rise to non-specular reflection with wavevectors and field polarisations mixed. The general formalism has already been fruitfully used for evaluating the effect of roughness on the Casimir force as well as the lateral Casimir force or Casimir torque appearing between corrugated surfaces. In this short review, we focus our attention on the case of the lateral force which should make possible in the future an experimental demonstration of the nontrivial (ie beyond PFA) interplay of geometry and Casimir effect.

This paper discusses recent developments on quantum electrodynamical (QED) phenomena, such as the Casimir effect, and their use in nanomechanics and nanotechnology in general. Casimir forces and torques arise from quantum fluctuations of vacuum or, more generally, from the zero-point energy of materials and their dependence on the boundary conditions of the electromagnetic fields. Because the latter can be tailored, this raises the interesting possibility of designing QED forces for specific applications. After a concise review of the field in an historical perspective, high precision measurements of the Casimir force using microelectromechanical systems (MEMS) technology and applications of the latter to nonlinear oscillators are presented, along with a discussion of its use in nanoscale position sensors. Then, experiments that have demonstrated the role of the skin-depth effect in reducing the Casimir force are presented. The dielectric response

The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the electromagnetic (EM) field in the intervening space. Thermal fluctuations of correlated fluids (such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are also modified by the boundaries, resulting in finite-size corrections at criticality, and additional forces that effect wetting and layering phenomena. Modified fluctuations of the EM field can also account for the 'van der Waals' interaction between conducting spheres, and have analogs in the fluctuation-induced interactions between inclusions on a membrane. We employ a path integral formalism to study these phenomena for boundaries of arbitrary shape. This allows us to examine the many unexpected phenomena of the dynamic Casimir effect due to moving boundaries. With the inclusion of quantum fluctuations, the EM vacuum behaves essentially as a complex fluid, and modifies the motion of objects through it. In particular, from the mechanical response function of the EM vacuum, we extract a plethora of interesting results, the most notable being: (i) The effective mass of a plate depends on its shape, and becomes anisotropic. (ii) There is dissipation and damping of the motion, again dependent upon shape and direction of motion, due to emission of photons. (iii) There is a continuous spectrum of resonant cavity modes that can be excited by the motion of the (neutral) boundaries.

We describe a superconducting Casimir apparatus inspired by a recently proposed setup
involving magnetic surfaces (Bimonte G 2014 Phys. Rev. Lett. 112 240401). The present
setup consists of a superconducting Nb sphere and a flat gold plate including in its interior a
superconducting Nb strip. The experimental scheme involves a differential measurement of
the Casimir force at a point of the gold plate above the Nb strip and away from it. We show
that similar to the previous setup, the superconducting system considered here implies widely
different modulations of the Casimir force, depending on whether the thermal force is
computed using the Drude or the plasma model, thus paving the way to an unambiguous
discrimination between these alternative prescriptions.

Although repulsive effects have been predicted for quantum vacuum forces between bodies with nontrivial electromagnetic properties, such as between a perfect electric conductor and a perfect magnetic conductor, realistic repulsion seems difficult to achieve. Repulsion is possible if the medium between the bodies has a permittivity in value intermediate to those of the two bodies, but this may not be a useful configuration. Here, inspired by recent numerical work, we initiate analytic calculations of the Casimir-Polder interaction between an atom with anisotropic polarizability and a plate with an aperture. In particular, for a semi-infinite plate, and, more generally, for a wedge, the problem is exactly solvable, and for sufficiently large anisotropy, Casimir-Polder repulsion is indeed possible, in agreement with the previous numerical studies. In order to achieve repulsion, what is needed is a sufficiently sharp edge (not so very sharp, in fact) so that the directions of polarizability of the conductor and the atom are roughly normal to each other. The machinery for carrying out the calculation with a finite aperture is presented. As a motivation for the quantum calculation, we carry out the corresponding classical analysis for the force between a dipole and a metallic sheet with a circular aperture, when the dipole is on the symmetry axis and oriented in the same direction.

We present a new method to compute quantum energies in presence of a background field. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Our procedure is applied to the study of the Casimir force between rigid bodies induced by a fluctuating real scalar field. We test our method with the classic parallel-plate configuration and study curvature effects quantitatively for the sphere-plate configuration. The numerical estimates are compared with the "proximity force approximation". Sizable curvature effects are found for a distance-tocurvature-radius ratio of a/R > 0.02.

The long-range interaction between two atoms and the long-range interaction between an ion and an electron are compared at small and large intersystem separations. The vacuum dressed atom formalism is applied and found to provide a framework for interpretation of the similarities between the two cases. The van der Waals forces or Casimir-Polder potentials are used to obtain insight into relativistic and higher multipolar terms.