Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called {\it sphere lattice regularization}, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do {\it not} take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warpedness parameter) and $T$(extra space IR parameter) dependence.
We examine the Casimir energy of 5D electro-magnetism in the recent standpoint. Z$_2$ symmetry is taken into account. After confirming the consistency with the past result, we do new things based on a new regularization. The regularization is based on the minimal area principle and the regularized configuration is the {\it sphere lattice}. We do it not in the Kaluza-Klein expanded form but in the closed form. The formalism is based on the heat-kernel approach using the position/momentum propagator. A useful expression of the Casimir energy, in terms of the P/M propagator, is obtained. Renormal…
We derive the electromagnetic self-energy and the radiative correction to the gyromagnetic ratio of a free electron using a Casimir energy approach. This method provides an attractive and straightforward physical basis for the renormalization process.
A technique for evaluating the electromagnetic Casimir energy in situations involving spherical or circular boundaries is presented. Zeta function regularization is unambiguously used from the start and the properties of Bessel and related zeta functions are central. Nontrivial results concerning these functions are given. While part of their application agrees with previous knowledge, new results like the zeta-regularized electromagnetic Casimir energy for a circular wire are included.
We apply a Casimir energy approach to evaluate the self-energy or one-photon radiative correction for an electron in a hydrogen orbital. This linking of the Lamb shift to the Casimir effect is obtained by treating the hydrogen orbital as a one-electron shell and including the probability of the electron being at a particular radius in that orbital and the probability that the electron will interact with a virtual photon of a given energy.
A simple, but effcient way of calculating regularized Casimir energies suitable for non-trivial frequency spectra is briefly described and applied to the case of a kappa-deformed scalar field theory. The results are consistent with the ones obtained by other means.
The electromagnetic Casimir energies of a spherical and a cylindrical cavity are analyzed semiclassically. The field theoretical self-stress of a spherical cavity with ideal metallic boundary conditions is reproduced to better than 1%. The subtractions in this case are unambiguous and the good agreement is interpreted as evidence that finite contributions from the exterior of the cavity are small. The semiclassical electromagnetic Casimir energy of a cylindrical cavity on the other hand vanishes to any order in the real reflection coefficients. The Casimir energy of a cylindrical cavity with a…
Quantum electrodynamic fields possess fluctuations corresponding to transient particle/antiparticle dipoles, which can be characterized by a non-vanishing polarizability density. Here, we extend a recently proposed quantum scaling law to describe the volumetric and radial polarizability density of a quantum field corresponding to electrons and positrons and derive the Casimir self-interaction energy (SIE) density of the field, $\bar{E}_{\rm{SIE}}$, in terms of the fine-structure constant. The proposed model obeys the cosmological equation of state $w=-1$ and the magnitude of the calculated $\b…
The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled massless scalars that satisfy conformally covariant boundary conditions. Surface contributions vanish for smooth metallic boundaries and the finite electromagnetic Casimir energy in leading semiclassical approximation is due to quadratic fluctuations about periodic rays in the interior of the cavity only. Semiclassically the non-vanishing Casimir…
By the thermofield dynamics (TFD) formalism we obtain the energy-momentum tensor for the Electromagnetism with Lorentz Breaking Even term of the Standard Model Extended (SME) Sector in a topology $S^{1}\times S^{1}\times R^{2}$. We carry out the compactification by a generalized TFD-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor, and the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and we remark the influence of the background in the traditional Casimir effect.
This paper studies two perfectly conducting parallel plates in the weak gravitational field on the surface of the Earth. Since the appropriate line element, to first order in the constant gravity acceleration g, is precisely of the Rindler type, we can exploit the formalism for studying Feynman Green functions in Rindler spacetime. Our analysis does not reduce the electromagnetic potential to the transverse part before quantization. It is instead fully covariant and well suited for obtaining all components of the regularized and renormalized energy-momentum tensor to arbitrary order in the gra…
A rigorous formulation of the problem of calculating the electromagnetic vacuum energy of an infinite dielectric cylinder is discussed. It is shown that the physically relevant spectrum of electromagnetic excitations includes the surface modes and photonic modes. The mathematical procedure of summing over this spectrum is proposed, and the transition to imaginary frequencies is accomplished. As a result, it is justified the imaginary-frequency representation for the vacuum energy which has been used in previous Casimir studies for this configuration.
The CPT-even sector of the standard model extension amounts to extending Maxwell electrodynamics by a gauge invariant term of the form $- \frac{1}{4} (k _{F}) _{αβμν} F ^{αβ} F ^{μν}$, where the Lorentz-violating (LV) background tensor $(k _{F}) _{αβμν}$ possesses the symmetries of the Riemann tensor. The electrodynamics in ponderable media is still described by Maxwell equations in matter with modified constitutive relations which depend on the coefficients for Lorentz violation. We study the effects of this theory on the Casimir force between two semi-infinite ponderable media. The Fresnel c…
Vacuum expectation values of the energy-momentum tensor and the Casimir forces are evaluated for scalar and electromagnetic fields in the geometry of two curved boundaries on background of the Robertson-Walker spacetime with negative spatial curvature. Robin boundary conditions are imposed in the case of the scalar field and perfect conductor boundary conditions are assumed for the electromagnetic field. We use the conformal relation between the Robertson-Walker and Rindler spacetimes and the corresponding results for two parallel plates moving with uniform proper acceleration through the Full…
In this paper we compute the leading order Casimir energy for the electromagnetic field (EM) in an open ended perfectly conducting rectangular waveguide in three spatial dimensions by a direct approach. For this purpose we first obtain the second quantized expression for the EM field with boundary conditions which would be appropriate for a waveguide. We then obtain the Casimir energy by two different procedures. Our main approach does not contain any analytic continuation techniques. The second approach involves the routine zeta function regularization along with some analytic continuation te…
We extend our previous work on a derivative expansion for the Casimir energy, to the case of the electromagnetic field coupled to two thin, imperfect mirrors. The latter are described by means of vacuum polarization tensors localized on the mirrors. We apply the results so obtained to compute the first correction to the proximity force approximation to the static Casimir effect.
Casimir entropy is an important aspect of casimir effect.In this paper,we employ the path integral method to derive the total relation for casimir entropy and internal energy of arbitrary shaped objects in the presence of two,three and four dimensions scalar fields and electromagnetic field.We obtain the casimir entropy and internal energy of two nanoribbon immersed in scalar field and two nanospheres immersed in scalar field and electromagnetic field.The casmir entropy of two nanospheres immersed in the electromagnetic field in small interval of temperature variations,shown a different behavi…
Using recently developed techniques based on scattering theory, we find the electromagnetic Casimir energy for geometries involving semi-infinite planes, a case that is of particular interest in the design of microelectromechanical devices. We obtain both approximate analytic formulae and exact results requiring only modest numerical computation. Using these results, we analyze the effects of edges and orientation on the Casimir energy. We also demonstrate the accuracy, simplicity, and utility of our approximation scheme, which is based on a multiple reflection expansion.
We calculate the total internal energy, total energy density and pressure, and the free energy for the neutrino and electromagnetic fields in Einstein and closed Friedmann cosmological models. The Casimir contributions to all these quantities are separated. The asymptotic expressions for both the total internal energy and free energy, and for the Casimir contributions to them are found in the limiting cases of low and high temperatures. It is shown that the neutrino field does not possess a classical limit at high temperature. As for the electromagnetic field, we demonstrate that the total int…
Casimir energy is calculated for the 5D electromagnetism in the warped geometry. It is compared with the flat case(arXiv:0801.3064). A new regularization, called sphere lattice regularization, is taken. It is based on the minimal area principle and is a direct realization of the geometrical approach to the renormalization group. The properly regularized form of Casimir energy, is expressed in a closed form. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of the Casimir energy. The warp parameter $\om$ suffers fr…
A general, exact formula is derived for the expectation value of the electromagnetic energy density of an inhomogeneous absorbing and dispersive dielectric medium in thermal equilibrium, assuming that the medium is well approximated as a continuum. From this formula we obtain the formal expression for the Casimir force density. Unlike most previous approaches to Casimir effects in which absorption is either ignored or admitted implicitly through the required analytic properties of the permittivity, we include dissipation explicitly via the coupling of each dipole oscillator of the medium to a …
In this paper we continue our program of computing Casimir self-entropies of idealized electrical bodies. Here we consider an electromagnetic $δ$-function sphere ("semitransparent sphere") whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by a plasma-like model. In the strong coupling limit, a perfectly conducting spherical shell is realized. We compute the entropy for both low and high temperatures. The TE self-entropy is negative as expected, but the TM self-entropy requires ultraviolet and infrared subtractions, and, surprisingly…
We calculate the Casimir interaction energy in $d=2$ spatial dimensions between two (zero-width) mirrors, one flat, and the other slightly curved, upon which {\em imperfect\/} conductor boundary conditions are imposed for an Electromagnetic (EM) field. Our main result is a second-order Derivative Expansion (DE) approximation for the Casimir energy, which is studied in different interesting limits. In particular, we focus on the emergence of a non-analyticity beyond the leading-order term in the DE, when approaching the limit of perfectly-conducting mirrors. We also show that the system conside…
The microscopic theory of the Casimir effect in the dielectric is studied in the framework when absorption is realized via a reservoir modeled by a set of oscillators with continuously distributed frquencies with the aim to see if the effects depend on the form of interaction with the reservoir. A simple case of the one-dimensional dielectric between two metallic plates is considered. Two possible models are investigated, the direct interaction of the electromagnetic field with the reservoir and indirect interaction via an intermediate oscillator imitating the atom. It is found that with the s…
The vacuum expectation value of the electromagnetic energy-momentum tensor between two parallel plates in spacetime dimensions D > 4 is calculated in the axial gauge. While the pressure between the plates agrees with the global Casimir force, the energy density is divergent at the plates and not compatible with the total energy which follows from the force. However, subtracting the divergent self-energies of the plates, the resulting energy is finite and consistent with the force. In analogy with the corresponding scalar case for spacetime dimensions D > 2, the divergent self-energy of a singl…
We compute the Casimir energy of the photon field in a de Sitter space and find it to be proportional to the size of the horizon, the same form of the holographic dark energy. We suggest to make metamaterials to mimic de Sitter space in laboratory and measure the predicted Casimir energy.
We consider the Casimir energy in a geometry of an infinite magnetodielectric wedge closed by a circularly cylindrical, perfectly conducting arc embedded in another magnetodielectric medium, under the condition that the speed of light be the same in both media. An expression for the Casimir energy corresponding to the arc is obtained and it is found that in the limit where the reflectivity of the wedge boundaries tends to unity the finite part of the Casimir energy of a perfectly conducting wedge-shaped sheet closed by a circular cylinder is regained. The energy of the latter geometry possesse…
We study the contribution of the thermal zero modes to the Casimir free energy, in the case of a fluctuating electromagnetic (EM) field in the presence of real materials described by frequency-dependent, local and isotropic permittivity ($ε$) and permeability ($μ$) functions. Those zero modes, present at any finite temperature, become dominant at high temperatures, since the theory is dimensionally reduced. Our work, within the context of the Derivative Expansion (DE) approach, focusses on the emergence of non analyticities in that dimensionally reduced theory. We conclude that the DE is well …
The wedge geometry closed by a circular-cylindrical arc is a nontrivial generalization of the cylinder, which may have various applications. If the radial boundaries are not perfect conductors, the angular eigenvalues are only implicitly determined. When the speed of light is the same on both sides of the wedge, the Casimir energy is finite, unlike the case of a perfect conductor, where there is a divergence associated with the corners where the radial planes meet the circular arc. We advance the study of this system by reporting results on the temperature dependence for the conducting situati…
We derive boundary conditions for electromagnetic fields on a $δ$-function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We unambiguously obtain the boundary conditions for a perfectly conducting $δ$-function plate in the limit of infinite dielectric response. We show that a material does not "optically vanish" in the thin-plate limit. The thin-plate limit of a plasma slab of thickness $d$ with plasma frequency $ω_p^2=ζ_p/d$ reduces to a $δ$-function plate for frequencies ($ω=iζ$) satisf…
We investigate the renormalized vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field inside and outside of a conducting cylindrical shell in the cosmic string spacetime. By using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases.
Mainly on nano-scale, but maybe not exclusively, it can be imagined a spontaneous charge disjunction inside certain media due to the fluctuations, collisions, wall effects, radiation or/and other presently unknown interactions. The repulsive Casimir-Lifshitz force may be also a good candidate as a source of this kind of phenomenon. To cover this assumption mathematically an additional term should appear in the Maxwell equations. As a consequence of this term, similar Klein-Gordon equations with a negative mass term will be obtained for the electric and magnetic fields. These equations may have…
The Casimir energy is evaluated for massless scalar fields under Dirichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on one and two infinite parallel plates moving by uniform proper acceleration through the Fulling--Rindler vacuum in an arbitrary number of spacetime dimension. For the geometry of a single plate the both regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are considered. The zeta function technique is used, in combination with contour integral representa…
Recently by us was proposed the model where Einstein's equation on the brane was connected with Maxwell's multi-dimensional equations in pseudo-Euclidean space. Based on this idea unification of 4-dimensional gravity and electromagnetism in (2+4)-space is found. In this picture photon is massless in four dimensions and obtains large mass in extra (1+1)-space normal to the brane.
