Casimir effect for regions with broken symmetry of boundaries

A method is proposed for computing corrections to the Casimir force caused by a broken symmetry of the boundaries. The values of these corrections are obtained for a parallelepiped in the case of scalar and electromagnetic fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 68–72, July, 1988.     

On a theory of the Casimir effect

We develop a mathematically precise framework for the Casimir effect. A major role is played by Dietz's idea of identifying the Casimir energy as the regularization-independent Ramanujan sum of an asymptotic series. As an illustration, we treat two cases: parallel plates and the sphere. We finally discuss the open problem of the Casimir force for the cube. We propose an Ansatz for the exterior force and argue why it may provide the exact solution, as well as an explanation of the repulsive sign of the force.     

Casimir effect in source theory

The theory of the Casimir effect, including its temperature dependence, is rederived by source theoretic methods, which do not employ the concept of zero point energy.Support in part by the National Science Foundation.     

Experiment and theory in the Casimir effect

Casimir effect is the attractive force which acts between two plane parallel, closely spaced, uncharged, metallic plates in vacuum. This phenomenon was predicted theoretically in 1948 and reliably investigated experimentally only in recent years. In fact, the Casimir force is similar to the familiar van der Waals force in the case of relatively large separations when the relativistic effects come into play. We review the most important experiments on measuring the Casimir force by means of torsion pendulum, atomic force microscope and micromechanical torsional oscillator. Special attention is paid to the puzzle of the thermal Casimir force, i.e. to the apparent violation of the third law of thermodynamics when the Lifshitz theory of dispersion forces is applied to real metals. Thereafter we discuss the role of the Casimir force in nanosystems including the stiction phenomenon, actuators, and interaction of hydrogen atoms with carbon nanotubes. The applications of the Casimir effect for constraining predictions of extra-dimensional unification schemes and other physics beyond the standard model are also considered.     

Casimir effect in source theory II

Another derivation is presented, one that emphasizes the physical normalization conditions, and employs a mathematical property of a theta function that originated with S. D. Poisson.     

Casimir effect in source theory III

A proper-energy method is used to find the energy of attraction between two dielectric slabs. Independent derivations of the attractive force are also presented.     

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.     

Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions

We consider the finite temperature Casimir effect of a massive fermionic field confined between two parallel plates, with MIT bag boundary conditions on the plates. The background spacetime is Mp+1×Tq which has q dimensions compactified to a torus. On the compact dimensions, the field is assumed to satisfy periodicity boundary conditions with arbitrary phases. Both the high temperature and the low temperature expansions of the Casimir free energy and the force are derived explicitly. It is found that the Casimir force acting on the plates is always attractive at any temperature regardless of the boundary conditions assumed on the compact torus. The asymptotic limits of the Casimir force in the small plate separation limit are also obtained.     

Casimir效应的另一种计算方法

利用Poisson求和公式和简单的正规化手续,给出了Casimir效应的另一种计算方法.     

Casimir effect for the sphere revisited

In a recent work Brevik et al. have offered formal proofs of two results which figure prominently in calculations of the Casimir pressure on a sphere. It is shown by means of simple counterexamples that each of those proofs is necessarily incorrect.     

Schwinger's method for the fermionic Casimir effect

The Casimir energy of a massive Dirac field confined between two parallel infinite plates is computed using a method proposed by Schwinger. The massless case is obtained as a limit of the massive case. The boundary conditions are those of zero current through the plates, as inspired by quark confinement in the MIT bag model for hadrons. We use an analytical continuation method of regularization which allows the employment of Epstein function techniques. The calculation using Schwinger's original regularization by a cutoff in proper time is also outlined.     

Casimir效应的一个简明计算

电磁场的真空态具有无穷大的能量,这个无穷大能量不可直接观测,只在某些特殊情况下才表现出可观测的效应,其中之一便是Casimir效应,通常这个效应的计算是在量子场论中,按重正化的办法进行,这里给出一个更为简明的算法。     

Schwinger's method for the massive Casimir effect

We apply a method recently proposed by Schwinger to the massive scalar field to calculate the Casimir effect. The method is applied with two different regularization schemes: Schwinger's original one by means of Poisson formula and another one by means of analytical continuation.     

Thermodynamics of the Casimir effect

A complete thermodynamic treatment of the Casimir effect is presented. Explicit expressions for the free and the internal energy, the entropy and the pressure are discussed. As an example we consider the Casimir effect with different temperatures between the plates (T) resp. outside of them (T'). For T'<T the pressure of heat radiation can eventually compensate the Casimir force and the total pressure can vanish. We consider both an isothermal and an adiabatic treatment of the interior region. The equilibrium point (vanishing pressure) turns out instable in the isothermal case. In the adiabatic situation we have both an instable and a stable equilibrium point, if T'/T is sufficiently small. Quantitative aspects are briefly discussed. Received 24 February 1999 and Received in final form 26 April 1999     

卡西米尔效应的格林函数计算方法

介绍了卡西米尔效应的严格格林函数表达式.作为应用,计算了4种边界条件下两平行板之间的卡西米尔能量.     

On Schwinger's method for obtaining the Casimir effect

We show that a slight modification in Schwinger's method leads directly to the finite result for the Casimir energy of a massless scalar theory.     

Cutoff dependence of the Casimir effect

The problem of calculating the Casimir force on two conducting planes by means of the stress tensor is examined. The evaluation of this quantity is carried out using an explicit regularization procedure which has its origin in the underlying (2+1) dimensional Poincaré invariance of the system. The force between the planes is found to depend on the ratio of two independent cutoff parameters, thereby rendering any prediction for the Casimir effect an explicit function of the particular calculational scheme employed. Similar results are shown to obtain in the case of the conducting sphere. Received: 15 October 2000 / Revised version: 10 January 2001 / Published online: 6 April 2001