The casimir effect as a screening effect in quantized field theory

We study the vacuum energy and the vacuum force in a system of quantized scalar fields (massive and massless) in interaction with a given screening medium. Regularization of the energy is studied and the types of determinable forces are clarified. The Casimir effect—the attraction between two conducting plates in a vacuum, and its extension to different geometries —is re-examined in this framework. Instead of the puzzling repulsion for a spherical shell conductor, an attractive force is obtained in our case. As a by-product, we obtain a potential energy between two balls of large screening power and at remote distance R, ?a₁a₂/4πR³, where a_i are the ball radii.     

Repulsive Casimir Force in a Cavity Comprising a Dielectric with Output Coupling

The Casimir force between a perfectly conducting wall and a dielectric wall in a cavity comprising a transparent dielectric with output coupling is investigated. By using full quantum theory, we obtain the analysis expression of the force, which shows that the interaction of the two walls in this system is always repulsive. And the value of the Casimir force varies with the field amplitude reflectivity and the cavity size.     

Repulsive Casimir Force in a Cavity Comprising a Dielectric with Output Coupling

The Casimir force between a perfectly conducting wall and a dielectric wall in a cavity comprising a transparent dielectric with output coupling is investigated. By using full quantum theory, we obtain the analysis expression of the force, which shows that the interaction of the two walls in this system is always repulsive. And the value of the Casimir force varies with the field amplitude reflectivity and the cavity size.     

Casimir forces between arbitrary compact objects

We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.     

二维情况下内部有质量费米子单圈图对Casimir力的贡献

采用Feynman的路径积分量子化方法,计算出两个平行的、理想的金属线之间,在绝对零度下量子电磁场在有质量费米子单圈图近似下的Casimir效应.     

Repulsive Maxwell-Chern-Simons Casimir effect

In the present Letter we discuss the role of different boundary conditions on the Casimir effect between parallel lines in a planar (2+1) system, specifically in the context of a Maxwell theory with a Chern-Simons mass term. We consider parallel lines of a different nature, namely a perfectly conducting line and an infinitely permeable one. We also discuss the case of two infinitely permeable lines. We compare our results with those found in the literature for the case of two perfectly conducting lines.     

Thermofield dynamics and Casimir effect for fermions

A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons [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 field in a d-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a three-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic box changes sign and estimate its value when the edge of the cube is of the order of the confining lengths for baryons.     

Measurement of the Casimir force between a gold sphere and a silicon surface with nanoscale trench arrays

We report measurements of the Casimir force between a gold sphere and a silicon surface with an array of nanoscale, rectangular corrugations using a micromechanical torsional oscillator. At distances between 150 and 500 nm, the measured force shows significant deviations from the pairwise additive formulism, demonstrating the strong dependence of the Casimir force on the shape of the interacting bodies. The observed deviation, however, is smaller than the calculated values for perfectly conducting surfaces, possibly due to the interplay between finite conductivity and geometry effects.     

Source Theory Treatment of the Casimir Effect: A Review

The general method to calculate Casimir forces using Source Theory is reviewed. Included are such issues as point splitting, high frequency cut-offs and the inclusion of temperature. The details of calculations for planar, spherical and cylindrical geometries are presented. Finally, assuming spin zero photons, the Casimir force between perfectly conducting spheres is calculated. The large distance behavior is found to be proportional to the inverse distance to the fourth power, unlike the spin one behavior of to the eighth power.     

Fermionic Casimir stress on a spherical bag

The zero-point energy due to quantum fluctuations in a massless fermionic field inside and outside an ideal spherical bag is computed. The result is a repulsive stress, the Casimir energy being , where a is the bag radius.     

The Casimir Effect for Parallel Plates in the Spacetime with a Fractal Extra Compactified Dimension

The Casimir effect for massless scalar fields satisfying Dirichlet boundary conditions on the parallel plates in the presence of one fractal extra compactified dimension is analyzed. We obtain the Casimir energy density by means of the regularization of multiple zeta function with one arbitrary exponent. We find a limit on the scale dimension like $\delta>\frac{1}{2}$ to keep the negative sign of the renormalized Casimir energy which is the difference between the regularized energy for two parallel plates and the one with no plates. We derive and calculate the Casimir force relating to the influence from the fractal additional compactified dimension between the parallel plates. The larger scale dimension leads to the greater revision on the original Casimir force. The two kinds of curves of Casimir force in the case of integer-numbered extra compactified dimension or fractal one are not superposition, which means that the Casimir force show whether the dimensionality of additional compactified space is integer or fraction.     

Casimir Energy for Spherical Shell in Schwarzschild Black Hole Background

In this paper, we consider the Casimir energy of massless scalar fields which satisfy the Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy.     

Zero-point energy of N perfectly conducting concentric cylindrical shells

The zero-point (Casimir) energy of N perfectly conducting, infinitely long, concentric cylindrical shells is calculated utilizing the mode summation technique. The obtained convergent expression is studied as a function of size, curvature and number of shells. Limiting cases, such as infinitely close shells or infinite radius shells are also investigated.     

Fermionic Casimir effect with helix boundary condition

In this paper, we consider the fermionic Casimir effect under a new type of space-time topology using the concept of quotient topology. The relation between the new topology and that in Feng and Li (Phys. Lett. B 691:167, 2010), Zhai et al. (Mod. Phys. Lett. A 26:669, 2011) is something like that between a Möbius strip and a cylindric. We obtain the exact results of the Casimir energy and force for the massless and massive Dirac fields in the (D+1)-dimensional space-time. For both massless and massive cases, there is a Z ₂ symmetry for the Casimir energy. To see the effect of the mass, we compare the result with that of the massless one and we found that the Casimir force approaches the result of the force in the massless case when the mass tends to zero and vanishes when the mass tends to infinity.     

A microscopic approach to Casimir and Casimir–Polder forces between metallic bodies

We consider the Casimir–Polder interaction energy between a metallic nanoparticle and a metallic plate, as well as the Casimir interaction energy between two macroscopic metal plates, in terms of the many-body dispersion interactions between their constituents. Expressions for two- and three-body dispersion interactions between the microscopic parts of a real metal are first obtained, both in the retarded and non-retarded limits. These expressions are then used to evaluate the overall two- and three-body contributions to the macroscopic Casimir–Polder and Casimir force, and to compare them with each other, for the two following geometries: metal nanoparticle/half-space and half-space/half-space, where all the materials are assumed perfect conductors. The above evaluation is obtained by summing up the contributions from the microscopic constituents of the bodies (metal nanoparticles). In the case of nanoparticle/half-space, our results fully agree with those that can be extracted from the corresponding macroscopic results, and explicitly show the non-applicability of the pairwise approximation for the geometry considered. In both cases, we find that, while the overall two-body contribution yields an attractive force, the overall three-body contribution is repulsive. Also, they turn out to be of the same order, consistently with the known non applicability of the pairwise approximation. The issue of the rapidity of convergence of the many-body expansion is also briefly discussed.     

Casimir Effect for a Perfectly Conducting Wedge in Terms of Local Zeta Function

The vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of calculations and gives rise to a finite expression for the energy density in question without any subtractions. Employment of the Hertz potentials for constructing the general solution to the Maxwell equations results in a considerable simplification of the calculations. Transition to the global zeta function is carried out by introducing a cutoff nearby the cusp at the origin. Proceeding from this the heat kernel coefficients are calculated and the high temperature asymptotics of the Helmholtz free energy and of the torque of the Casimir forces are found. The wedge singularity gives rise to a specific high temperature behavior ∼T2 of the quantities under consideration. The obtained results are directly applicable to the free energy of a scalar massless field and electromagnetic field on the background of a cosmic string.     

The Casimir Effect and the Vacuum Energy: Duality in the Physical Interpretation

The Casimir effect is usually interpreted as arising from the modification of the zero point energy of QED when two perfectly conducting plates are put very close to each other, and as a proof of the “reality” of this zero point energy. The Dark Energy, necessary to explain the acceleration of the expansion of the Universe is sometimes viewed as another proof of the same reality. Recently, several physicists have challenged the usual interpretation, arguing that the Casimir effect should rather be considered as a “giant” van der Waals effect. All these aspects are shortly reviewed.     

Surface plasmon modes and the Casimir energy

We show the influence of surface plasmons on the Casimir effect between two plane parallel metallic mirrors at arbitrary distances. Using the plasma model to describe the optical response of the metal, we express the Casimir energy as a sum of contributions associated with evanescent surface plasmon modes and propagative cavity modes. In contrast to naive expectations, the plasmonic mode contribution is essential at all distances in order to ensure the correct result for the Casimir energy. One of the two plasmonic modes gives rise to a repulsive contribution, balancing out the attractive contributions from propagating cavity modes, while both contributions taken separately are much larger than the actual value of the Casimir energy. This also suggests possibilities to tailor the sign of the Casimir force via surface plasmons.     

Calculation of the regularized vacuum energy in cavity field theories

A novel technique based on Schwinger's proper time method is applied to the Casimir problem of the M.I.T. bag model. Calculations of the regularized vacuum energies of massless scalar and Dirac spinor fields confined to a static and spherical cavity are presented in a consistent manner. While our results agree partly with previous calculations based on asymptotic methods, the main advantage of our technique is that the numerical errors are under control. Interpreting the bag constant as a vacuum expectation value, we investigate potential cancellations of boundary divergences between the canonical energy and its bag constant counterpart in the fermionic case. It is found that such cancellations do not occur. Received: 19 March 1999 / Published online: 28 September 1999