Narrow Results

Since its first description in 1948, the Casimir effect has been studied extensively. Standard arguments for its existence hinge on the elimination of certain modes of the electromagnetic field because of the boundary conditions in the Casimir cavity. As such, it has been suggested that the ground state energy of the vacuum within the cavity may be reduced compared to the value outside. Could this have an effect on physical phenomena within the cavity? We study this Casimir energy and probe whether the critical temperature $T_c$ of a superconductor is altered when it is placed in the cavity. We do not detect any change in $T_c$ larger than 12$\mu$K, but theoretically expect a change on the order of 0.025$\mu$K, roughly 1000 times lower than our achieved sensitivity.

In this paper, we calculate the radiative correction to the Casimir energy for both massive and massless Lorentz-violating scalar fields confined between two membranes with rough surfaces in a (3+1)-dimensional spacetime. The computations are performed for four types of boundary conditions: Dirichlet, Neumann, Periodic, and Mixed. A crucial element of our approach involves the use of position-dependent counterterms to incorporate the influence of boundaries within the renormalization program. To manage the divergences that emerge in the Casimir energy calculations, we apply the Box Subtraction Scheme (BSS) along with the cutoff regularization technique. We present and discuss results for various degrees of membrane roughness, emphasizing the consistency of our findings with theoretical expectations.

In this paper, we review the calculations that are needed to obtain the bosonic and fermionic effective potential at finite temperature and volume (at one loop). The calculations at finite volume correspond to S¹ × R^d topology. These calculations appear in the calculation of the Casimir energy and of the effective potential of extra dimensional theories. In the case of finite volume corrections, we impose twisted boundary conditions and obtain semi-analytic results. We mainly focus in the details and validity of the results. The zeta function regularization method is used to regularize the infinite summations. Also the dimensional regularization method is used in order to renormalize the UV singularities of the integrations over momentum space. The approximations and expansions are carried out within the perturbative limits. After the end of each section, we briefly present applications associated to the calculations. Particularly the calculation of the effective potential at finite temperature for the standard model fields, the effective potential for warped and large extra dimensions, and the topological mass creation. In the end, we discuss on the convergence and validity of one of the obtained semi-analytic results.

The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically for the first time for an arbitrary physically possible frequency dispersion of dielectric permittivity ε(iω). A microscopic model of dielectrics is considered, divergences are absent in calculations because an average interatomic distance λ is a physical cutoff in the theory. This fact has been overlooked earlier, which led to divergences in various macroscopic approaches to the Casimir energy of connected dielectrics.

We re-evaluate the zero point Casimir energy for the case of a massive scalar field in R¹×S³ space, allowing also for deviations from the standard conformal value ξ=1/6, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularization of the vacuum energy, as conjectured in a previous publication. The analytic continuation can be performed in two ways, which are seen to be equivalent.

Casimir vacuum energy is divergent. It needs to be regularized. The regularization introduces a renormalization scale which may lead to a scale dependent cosmological constant. We show that the requirement of physical cosmological constant is renormalization scale independent provides important constraints on possible particle contents and their masses in particle physics models. In the Standard Model of strong and electroweak interactions, besides the Casimir vacuum energy there is also vacuum energy induced from spontaneous symmetry breaking. The requirement that the total vacuum energy to be scale independent dictates the Higgs mass to be where the summation is over fermions and N_i equals to 3 and 1 for quarks and leptons, respectively. The Higgs mass is predicted to be approximately 382 GeV.

Recently it was suggested that the dark energy maybe related to the well-known hierarchy between the Planck scale (~ 10¹⁹GeV) and the TeV scale. The same brane-world setup to address this hierarchy problem may also in principle address the smallness problem of dark energy. Specifically, the Planck-SM hierarchy ratio was viewed as a quantum gravity-related, dimensionless fine structure constant where various physical energy scales in the system are associated with the Planck mass through different powers of the 'gravity fine structure constant'. In this paper we provide a toy model based on the Randall-Sundrum geometry where SUSY-breaking is induced by the coupling between a SUSY-breaking Higgs field on the brane and the KK gravitinos. We show that the associated Casimir energy density indeed conforms with the dark energy scale.

In this paper we study the Casimir force for a piston configuration in R³ with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is "free to move" along a transverse dimension to the curved one and in the other case the piston "moves" along the curved one. We find that the Casimir force has opposite signs in the two cases. We also use a semi-analytic method to study the Casimir energy and force. In addition we discuss some topics for the aforementioned piston configuration in R³ and for possible modifications from extra dimensional manifolds.

We calculate the scalar Casimir energy for a Minkowski spacetime with T^d × S_FZ as extra dimensional space, with T^d the d-dimensional commutative torus and S_FZ the noncommutative two-sphere. We compute the Casimir energy up to one-loop level in order to address the stabilization of the internal space issue. We found that, contrary to the noncommutative two-torus case, the one-loop Casimir energy is singular, when D = even, therefore cannot give reliable results, when D = 4. However, when D = odd and d = even, the Casimir energy is always regular and a stabilization radius for the internal commutative space exists.

In [B. Nazari, Mod. Phys. Lett. A31, 1650007 (2016)], we calculated finite temperature corrections to the energy of the Casimir effect of two conducting parallel plates in a general weak gravitational field. The calculations was done for the case a scalar field was present between the plates. Here we find the same results in the presence of an electromagnetic field.

In this paper, the first-order radiative correction to the Casimir energy for a massive scalar field in the ${\varphi }^4$ theory on a spherical surface with $S^2$ topology was calculated. In common methods for calculating the radiative correction to the Casimir energy, the counter-terms related to free theory are used. However, in this study, by using a systematic perturbation expansion, the obtained counter-terms in renormalization program were automatically position-dependent. We maintained that this dependency was permitted, reflecting the effects of the boundary conditions imposed or background space in the problem. Additionally, along with the renormalization program, a supplementary regularization technique that we named Box Subtraction Scheme (BSS) was performed. This scheme presents a useful method for the regularization of divergences, providing a situation that the infinities would be removed spontaneously without any ambiguity. Analysis of the necessary limits of the obtained results for the Casimir energy of the massive and massless scalar field confirmed the appropriate and reasonable consistency of the answers.

This comment is devoted to the recalculation of the Casimir energy of a massless scalar field in the Kerr black hole surrounded by quintessence derived in [B. Toshmatov, Z. Stuchlík and B. Ahmedov, Eur. Phys. J. Plus132, 98 (2017)] and its comparison with the results recently obtained in [V. B. Bezerra, M. S. Cunha, L. F. F. Freitas and C. R. Muniz, Mod. Phys. Lett. A32, 1750005 (2017)] in the spacetime [S. G. Ghosh, Eur. Phys. J. C76, 222 (2016)]. We have shown that in the more realistic spacetime which does not have the failures illustrated here, the Casimir energy is significantly bigger than that derived in [V. B. Bezerra, M. S. Cunha, L. F. F. Freitas and C. R. Muniz, Mod. Phys. Lett. A32, 1750005 (2017)], and the difference becomes crucial especially in the regions of near horizons of the spacetime.

The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel–Plana formula is used for renormalization of divergent series in the condensate calculation. A differential relation between the static Casimir energy density and static Casimir condensate is derived.

The Casimir energy is constructed for a system consisting of two semi-infinite slabs of anisotropic material. Each of them is characterized by bulk complex dielectric permittivity tensor and surface conductivity on the free boundary. We found general form of the scattering matrix and Fresnel coefficients for each part of the system by solving Maxwell equations in the anisotropic media.

The renormalization program in every renormalized theory should run consistently with the type of boundary condition imposed on quantum fields. To maintain this consistency, the counterterms usually appear in the position-dependent form. In this study, using such counterterms, we calculated the radiative correction to the Casimir energy for massive and massless Lorentz-violating scalar field constrained with Dirichlet boundary condition between two parallel plates in $d$ spatial dimensions. In the calculation procedure, to remove infinities appearing in the vacuum energies, the box subtraction scheme (BSS) supplemented by the cutoff regularization technique and analytic continuation technique was employed. Normally, in the BSS, two similar configurations are defined and their vacuum energies are subtracted from each other in the appropriate limits. Our final results regarding all spatial dimensions were convergent and consistent with the expected physical basis. We further plotted the Casimir energy density for the time-like and space-like Lorentz-violating systems in a number of odd and even dimensions; multiple aspects of the obtained results were ultimately discussed.

Wormholes (WHs) require negative energy, and therefore an exotic matter source. Since Casimir energy is negative, it has been speculated as a good candidate to source those objects a long time ago. However, only very recently, a full solution for $D=4$ has been found by [R. Garattini, Eur. Phys. J. C79, 951 (2019), doi:10.1140/epjc/s10052-019-7468-y] thus the Casimir energy can be a source of traversable WHs. Soon later [G. Alencar, V. B. Bezerra and C. R. Muniz, arXiv:2104.13952 [gr-qc]] have shown, that this is not true in $D=3$. In this paper, we show that Casimir energy can be a source of the Morris–Thorne WH for all spacetime with $D>3$. Finally, we add the cosmological constant and find that for $D=3$ Casimir WHs are possible, however, the space must always be AdS. For $D>3$, we show that the cosmological constant invert the signal with increasing throat size.

We consider the brane universe in the bulk background of the topological Reissner–Nordström de Sitter black holes. We show that the thermodynamic quantities (including entropy) of the dual CFT take usual special forms expressed in terms of Hubble parameter and its time derivative at the moment, when the brane crosses the black hole horizon or the cosmological horizon. We obtain the generalized Cardy–Verlinde formula for the CFT with a charge and cosmological constant, for any values of the curvature parameter k in the Friedmann equations.

We consider the ground state energy of a spinor field in the background of a square well-shaped magnetic flux tube. We use the zeta-function regularization and express the ground state energy as an integral involving the Jost function of a two-dimensional scattering problem. We perform the renormalization by subtracting the contributions from first several heat kernel coefficients. The ground state energy is presented as a convergent expression suited for numerical evaluation. We discuss corresponding numerical calculations. Using the uniform asymptotic expansion of the special functions entering the Jost function we are able to calculate higher order heat kernel coefficients.

Quantum vacuum energy entered hadronic physics through the zero-point energy parameter introduced into the bag model. Estimates of this parameter led to apparent discordance with phenomenological fits. More serious were divergences which were omitted in an ad hoc manner. New developments in understanding Casimir self-stresses, and the nature of surface divergences, promise to render the situation clearcut.

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 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 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 Λ(4D UV-cutoff), ω(5D bulk curvature, warpedness parameter) and T(extra space IR parameter) dependence.