Violation of the Lorentz symmetry has important effects on physical quantities including field propagators. Therefore, in addition to the leading order, the sub-leading order of quantities may be modified. In this paper, we calculate the next to leading (NLO) radiative corrections to the Casimir energy in the presence of two perfectly conducting parallel plates for $ϕ^4$ theory with a Lorentz-breaking extension. We do the renormalization and investigate these NLO corrections for three distinct directions of the Lorentz violation; temporal direction, parallel and perpendicular to the plates.
This paper investigates the Casimir Energy modifications due to the Lorentz-violating CPT-even contribution in an extension of the scalar QED. We have considered the complex scalar field satisfying Dirichlet boundary conditions between two parallel plates separated by a small distance. An appropriate tensor parametrization allowed us to study the Casimir effect in three setups: isotropic, anisotropic parity-odd, and anisotropic parity-even. We have shown that the Lorentz-violating contributions promote increased Casimir energy for both the isotropic and anisotropic parity-odd configurations. H…
In this paper we consider a Lorentz-breaking extension of the theory for a real massive scalar quantum field in the region between two large parallel plates, with our manner to break the Lorentz symmetry is CPT-even, aether-like. For this system we calculated the Casimir energy considering different boundary conditions. It turns out to be that the Casimir energy strongly depends on the direction of the constant vector implementing the Lorentz symmetry breaking, as well as on the boundary conditions.
Following a field-theoretical approach, we study the scalar Casimir effect upon a perfectly conducting cylindrical shell in the presence of spontaneous Lorentz symmetry breaking. The scalar field is modeled by a Lorentz-breaking extension of the theory for a real scalar quantum field in the bulk regions. The corresponding Green's functions satisfying Dirichlet boundary conditions on the cylindrical shell are derived explicitly. We express the Casimir pressure (i.e. the vacuum expectation value of the normal-normal component of the stress-energy tensor) as a suitable second-order differential o…
The renormalization program in every renormalized theory should be 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 the present 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 sub…
In this paper I study the Casimir effect caused by a charged and massive scalar field that breaks Lorentz invariance in a CPT-even, aether-like manner. I investigate the case of a scalar field that satisfies Dirichlet or mixed (Dirichlet-Neumann) boundary conditions on a pair of very large plane parallel plates. The case of Neumann boundary conditions is straightforward and will not be examined in detail. I use the $ζ$-function regularization technique to study the effect of a constant magnetic field, orthogonal to the plates, on the Casimir energy and pressure. I investigate the cases of a ti…
We study the Casimir effect in the classical geometry of two parallel conductive plates, separated by a distance $L$, for a Lorentz-breaking extension of the scalar field theory. The Lorentz-violating part of the theory is characterized by the term $λ\left( u \cdot \partial ϕ\right )^{2}$, where the parameter $λ$ and the background four-vector $u ^μ$ codify Lorentz symmetry violation. We use Green's function techniques to study the local behavior of the vacuum stress-energy tensor in the region between the plates. Closed analytical expressions are obtained for the Casimir energy and pressure. …
One-Loop Correction to the Casimir Energy in Lorentz-Violating $ϕ^4$ Theory with Rough Membrane Boundaries
Department of Physics, Semnan Branch, Islamic Azad University, Semnan, Iran（伊斯兰阿扎德大学塞姆南分校物理系）；Energy and Sustainable Development Research Center, Semnan Branch, Islamic Azad University, Semnan, Iran（伊斯兰阿扎德大学塞姆南分校能源与可持续发展研究中心）
Fermionic Casimir effect in an axial Lorentz-violating background
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Universidade Estadual da Paraíba (UEPB), Centro de Ciências Exatas e Sociais Aplicadas (CCEA)（帕拉伊巴州立大学精确科学与社会科学中心）；Departamento de Física, Universidade Federal da Paraíba（帕拉伊巴联邦大学物理系）
In this work I investigate the finite temperature Casimir effect due to a massive and charged scalar field that breaks Lorentz invariance in a CPT-even, aether-like way. I study the cases of Dirichlet and mixed (Dirichlet-Neumann) boundary conditions on a pair of parallel plates. I will not examine the case of Neumann boundary conditions since it produces the same results as Dirichlet boundary conditions. The main tool used in this investigation is the $ζ$-function technique that allows me to obtain the Helmoltz free energy and Casimir pressure in the presence of a uniform magnetic field perpe…
The Casimir effect is one of the most remarkable consequences of the non-zero vacuum energy predicted by quantum field theory. In this paper we use a local approach to study the Lorentz violation effects of the minimal standard model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method similar to that used for obtaining the Born series for the scattering amplitudes in quantum mechanics, we compute, at leading order in the Lorentz-violating coefficients, the relevant Green's function which satisfies given boundary conditions. The stand…
We investigate the Casimir effect, due to the confinement of a scalar field in a $D$-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by the term $λ(u \cdot \partial ϕ) ^{2}$, where the parameter $λ$ and the background vector $u^μ$ codify the breakdown of Lorentz symmetry. We compute, as a function of $D$, the Casimir stress by using Green's function techniques for two specific choices of the vector $u ^μ$. In the timelike case, $u ^μ = (1,0,...,0)$, the Casimir stress can be factorized as the product of the Lorentz invariant result time…
One of the challenges in connecting higher dimensional theories to cosmology is stabilization of the moduli fields. We investigate the role of a Lorentz violating vector field in the context of stabilization. Specifically, we compute the one loop Casimir energy in Randall-Sundrum 5-dimensional (non-supersymmetric) S^1/ Z_2 orbifolds resulting from the interaction of a real scalar field with periodic boundary conditions with a Lorentz violating vector field. We find that the result is an enhanced attractive Casimir force. Hence, for stability, positive contributions to the Casimir force from br…
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…
We study the Casimir effect in the framework of Standard Model Extension (SME). Employing the weak field approximation, the vacuum energy density ε and the pressure for a massless scalar field confined between two nearby parallel plates in a static spacetime background are calculated. In particular, through the analysis of ε, we speculate a constraint on the Lorentz-violating term s00 which is lower than the bounds currently available for this quantity. After that, the correction to the pressure given by the gravitational sector of SME is presented. Finally, we remark that our outcome has an i…
Recently a great deal of interest in field theories formulated in a Lorentz violating framework has been developed. Here the Very Special Relativity (VSR) is considered. The main aspect in the VSR proposal is that laws of physics are invariant under the subgroups of the Poincaré group preserving the basic elements of special relativity. An important point is that the photon acquires a mass. In this context, the energy-momentum tensor for the electromagnetic field is calculated. From this, the Stefan-Boltzmann law and Casimir effect at finite temperature in VSR are obtained. The effects of temp…
Universidade Federal de Mato Grosso（马托格罗索联邦大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Khazar University（阿塞拜疆可汗大学）
Probing Lorentz symmetry violation via the Casimir effect in rectangular cavities
Universidade Estadual da Paraíba (UEPB)（帕拉伊巴州立大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）
We present calculations of Casimir energy (CE) in a system of quantized electromagnetic (EM) field interacting with an infinite circular cylindrical shell (which we call `the defect'). Interaction is described in the only QFT-consistent way by Chern-Simon action concentrated on the defect, with a single coupling constant $a$. For regularization of UV divergencies of the theory we use % physically motivated Pauli-Villars regularization of the free EM action. The divergencies are extracted as a polynomial in regularization mass $M$, and they renormalize classical part of the surface action. We r…
Within the framework of the (3+1)-dimensional Lorentz-violating extended electrodynamics including the CPT-odd Chern-Simons term, we consider the electromagnetic field between the two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. We also show that the tachyon-induced vacuum instability vanishes when the separation between the plates is sufficiently small though finite. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over…
The Thermofield Dynamics (TFD) formalism is considered. In this context, a Lorentz-breaking scalar field theory is introduced. In contrast to the Matsubara formalism, the best-known approach to introducing the temperature effect, TFD is a real-time formalism and is a topological field theory. While in Matsubara the temperature effects are introduced as a consequence of a compactification of the field in a finite interval on the time axis, in the TFD this effect emerges through a condensed state related to the Bogoliubov transformation. An advantage of the TFD formalism is that different topolo…
In our five-dimensional cosmological model, we investigate the role of a Lorentz violating vector "æther" field on the moduli stabilization mechanism. We consider the case of a space-like æther field on a compact circle with Maxwell-type kinetic term. The Casimir energy of certain combinations of massless and massive bulk fields generates a stabilizing potential for the radius of the compact direction while driving the accelerated expansion in the non-compact directions. It is shown that the æther field can reduce the influence of the Casimir force and slow down the oscillation of the radion f…
With an emphasis on unitarity and CPT requirements, we study the inclusion of CP-violating processes in baryogenesis at next-to-leading order, particularly those involving the top Yukawa interaction in leptogenesis. We show that there are more contributions than previously considered, but also important cancellations. Some of these involve the interference of connected with disconnected diagrams. We also discuss on the application of the Kinoshita-Lee-Nauenberg theorem to treat the infrared divergences that are common at next-to-leading order. Finally, we calculate the CP asymmetry in the thre…
We compute the full ${\cal O}(α_s^4)$ and ${\cal O}(α_s^4\logα_s)$ corrections to the potential $V_R(r)$ between the static color sources, where $V_R(r)$ is defined from the Wilson loop in a general representation $R$ of a general gauge group $G$. We find a violation of the Casimir scaling of the potential, for the first time, at ${\cal O}(α_s^4)$. The effect of the Casimir scaling violation is predicted to reduce the tangent of $V_R(r)/C_R$ proportionally to specific color factors dependent on $R$. We study the sizes of the Casimir scaling violation for various $R$'s in the case $G=SU(3)$. We…
We investigate the role of Casimir energy as a mechanism for brane stability in five-dimensional models with the fifth dimension compactified on an S^1\Z_2 orbifold, which includes the Randall-Sundrum two brane model (RS1). We employ a zeta-function regularization technique utilizing the Schwinger proper time method and the Jacobi theta function identity to calculate the one-loop effective potential. We show that the combination of the Casimir energies of a scalar Higgs field, the three generations of Standard Model fermions and one additional massive non-SM scalar in the bulk produce a non-tr…
We present a class of nonsingular, bouncing cosmologies that evade singularity theorems through the use of vorticity in compact extra dimensions. The vorticity combats the focusing of geodesics during the contracting phase. The construction requires fluids that violate the null energy condition (NEC) in the compact dimensions, where they can be provided by known stable NEC violating sources such as Casimir energy. The four dimensional effective theory contains an NEC violating fluid of Kaluza-Klein excitations of the higher dimensional metric. These spacetime metrics could potentially allow dy…
Lorentz-violating modifications to particle dynamics, thermodynamics and vacuum energy in bumblebee gravity
Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Khazar University（哈扎尔大学）；Eastern Mediterranean University（东地中海大学）；University of Hradec Králové（赫拉德茨-克拉洛韦大学）；Al-Farabi Kazakh National University（阿里-法拉比哈萨克国立大学）
