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.     

Proper Dirac quantization of a free particle on a D-dimensional sphere

We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in D dimensions is possible only by converting the constraints to Abelian gauge constraints, which are of first class in Dirac's classification scheme. The energy spectrum is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere. A quantization of Dirac's modified Poisson brackets for second-class constraints is also possible and unique, but must be rejected since the resulting energy spectrum is physically incorrect.     

Weak Gravitational Wave and Casimir Energy of a Scalar Field

In this paper, we calculate the effect of a weak gravitational field on the Casimir force between two ideal plates subjected to a massless minimally coupled field. It is the aim of this work to study the Casimir energy under a weak perturbation of gravity. Moreover, the fluctuations of the stress-energy tensor for a scalar field in de Sitter space-time are computed as well.     

Dynamical Casimir Effect for Scalar Fields I (Particle Creation)

The dynamical Casimir effect for neutral scalar massive field in a cavity with perfect reflecting boundaries is revisited from a mathematical point of view. We consider some 1+1 and 3+1 dimensional examples in which the boundary oscillates. For short times, the average number of produced particles is calculated using the second order perturbation theory, and for large times, the method to calculate the number of created particles is the rotating wave approximation. PACS Subject Classifications. 42.50.Lc,03.70.+k,11.10.Ef     

Dynamical Casimir Effect for Scalar Fields II (Energy Calculation)

The energy of the evolved vacuum state is calculated. From a frequency cut-off regularisation the divergent terms are separated and, in the 1 + 1 dimensional case they are removed with a mass renormalisation of the moving boundary. A renormalisation of the external force is also needed in 3 + 1 dimensions. PACS Subject Classifications: 42.50.Lc, 03.70.+k, 11.10.Ef.     

Riccion from higher-dimensional space-time with D-dimensional sphere as a compact manifold and one-loop renormalization

Lagrangian density of riccions is obtained with the quartic self-interacting potential using higher-derivative gravitational action in (4 +D)-dimensional space-time withS ^D as a compact manifold. It is found that the resulting four-dimensional theory for riccions is one-loop multiplicatively renormalizable. Renormalization group equations are solved and its solutions yield many interesting results such as (i) dependence of extra dimensions on the enegy mass scale showing that these dimensions increase with the increasing mass scale up toD = 6, (ii) phase transition at 3.05 × 10¹⁶ GeV and (iii) dependence of gravitational and other coupling constants on energy scale. Results also suggest that space-time above 3.05 × 10¹⁶ GeV should be fractal. Moreover, dimension of the compact manifold decreases with the decreasing energy mass scale such thatD = 1 at the scale of the phase transition. Results imply invisiblity of S¹ at this scale (which is 3.05 × 10¹⁶ GeV).     

Casimir Effect of Scalar Field on Sn-1 Manifold

Casimir effect of scalar field on R⁴×S_n-1 manifolds is evaluated. The results show that compactness of manifolds S₁ and S₂ can be held by Casimir force. However, other compact spaces (S_n-1, n > 3 ) are unstable.     

Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space

The Casimir stress on a cylindrical shell in background of conformally flat spacetime for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition, formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.     

Casimir effect for a scalar field via Krein quantization

In this work, we present a rather simple method to study the Casimir effect on a spherical shell for a massless scalar field with Dirichlet boundary condition by applying the indefinite metric field (Krein) quantization technique. In this technique, the field operators are constructed from both negative and positive norm states. Having understood that negative norm states are un-physical, they are only used as a mathematical tool for renormalizing the theory and then one can get rid of them by imposing some proper physical conditions.     

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.     

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.     

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.     

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.     

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.     

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.     

Modified cell theory: Free volume distributions and the equation of state for D-dimensional hard sphere systems

A generalized cell model, using cells of different sizes, is applied to hard rods, disks and spheres. Structures is discussed in terms of free volumes. The derived equation of state is exact for rods. For disks and spheres it provides a good approximation in the dense fluid and solid state.