arXiv subjects

E. R. Bezerra de Mello

Publications and source records attributed to E. R. Bezerra de Mello.

At least 19 recordsLinked to original sources

arXiv2026

Vacuum polarization by charged matter fields in AdS spacetime in the presence of a cosmic string

In this paper we revisited the analyse the vacuum polarizations effect associated wit charged matter fields in a higher-dimensional anti de-Sitter (AdS) spacetime in the presence of an idealized cosmic string carrying magnetic flux running along its core. Specifically we will consider, separately, charged bosonic and fermionic fields propagating in this manifold. Our main objective is to calculate the vacuum expectation values (VEV) of the energy-momentum tensor, $\langle T^μ_ν\rangle$, associated with both matters fields. As will see, these VEVs are even function of the magnetic flux running along the string's core, with period equal to the quantum flux $Φ_0=\frac{2π}{e}$. Because the results obtained are expressed in terms of special functions, and a clear behavior for them are not very enlightening, we provide some graphs exhibiting their behavior as function of the distance to the string considering different values for the parameters presented in the model considered.

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arXiv2026

Casimir effect for a massive scalar field confined between parallel plates with a spatially varying effective mass

We investigate the Casimir effect for a massive real scalar field confined between two perfectly reflecting parallel plates in the presence of a position-dependent effective mass, a mechanism for coupling a scalar background to a scalar field. Exact normal modes are obtained by solving the corresponding Klein-Gordon equation, leading to a transverse energy spectrum that exhibits a characteristic Landau-like structure despite the absence of an external magnetic field. Upon quantization of the field, the vacuum energy is evaluated by means of generalized zeta-function regularization together with an appropriate renormalization procedure. The renormalized vacuum energy naturally separates into a Landau-like contribution and an additional term induced by the spatial dependence of the effective mass. We show analytically and numerically that both contributions are exponentially suppressed in the strong-coupling regime. In the opposite limit, the Landau-like contribution smoothly reproduces the standard vacuum energy for a massive scalar field confined between parallel plates, whereas the additional contribution becomes singular owing to the restricted domain of validity of the exact spectrum. Except in the vicinity of this singular limit, the vacuum energy is shown to be dominated by the Landau-like sector. Our results establish a direct connection between position-dependent effective masses and boundary-induced quantum vacuum phenomena, providing a new exactly solvable framework for the investigation of Casimir effects in spatially inhomogeneous relativistic systems.

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arXiv2026

Fermionic Casimir effect in an axial Lorentz-violating background

We investigate the fermionic Casimir effect for a Dirac field confined between two parallel plates with MIT bag boundary conditions in the presence of CPT-odd Lorentz-symmetry violation described by a constant axial background vector $b_μ$. The exact mode quantization is derived from the modified Dirac equation in the planar geometry, and the vacuum energy is formulated through a phase-shift representation. For spacelike backgrounds we show that the components parallel to the plates can be absorbed into a shift of the transverse momenta and therefore do not affect the renormalized Casimir energy, while the component normal to the plates modifies the longitudinal spectrum and produces a genuine Lorentz-violating correction. Both the timelike component $b_{0}$ and the normal spacelike component $b_{z}$ can thus be treated within a unified framework characterized by a single effective spectral parameter. A closed logarithmic integral representation for the Casimir energy is obtained and its behavior is analyzed in the Lorentz-symmetric, weak-background, and strong-background regimes.

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arXiv2026

Induced current by a magnetic flux in $(1+2)-$dimensional conical spacetime in a Ho{ř}ava-Lifshitz Lorentz-violating scenario

We investigate the vacuum expectation value of bosonic current induced by a magnetic flux in a $(2+1)-$dimensional conical spacetime in the presence of a circular boundary, in a Ho{ř}ava-Lifshitz Lorentz violation symmetry scenario. We assume that the circular boundary is concentric with magnetic flux, and the massive scalar quantum field obeys the Robin boundary condition on the boundary. In order to develop this analysis, we calculate the positive frequency Wightman functions for both regions, inside and outside the boundary. Using these functions, we obtain analytical expressions for the vacuum expectation bosonic currents. As we will see, these functions are presented in the form of the sum of boundary-free and boundary-induced parts. As to the boundary-induced currents, some asymptotic behaviors are investigated for specific limiting cases; moreover, in order to provide a better understanding about the behavior of the currents, some plots are given.

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arXiv2026

Thermal correction on the Casimir energy in a Horava-Lifshitz Lorentz-violating scenario

The Casimir effect is considered a great triumph of Quantum Field Theory. Originally the Casimir energy was investigated considering the vacuum fluctuation associated with electromagnetic field; however it has also been analyzed considering different type of quantum fields. More recently the Casimir energy was studied in the context of Lorentz symmetry violation. In this work we investigate the effect of finite temperature on the Casmir energy considering a Lorenttz violation symmetry in a Horava-Lifshitz scenario. In this sense we consider a massive scalar quantum field confined in a region between two large and parallel plates. So our main objective is to investigate how, in this Lorentz violation scenario (LV), the Casimir energy depends on the temperature. Another point to be analyzed, is influence of the parameter associated with the LV, $ξ$, in the thermal correction.

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arXiv2026

Probing Lorentz symmetry violation via the Casimir effect in rectangular cavities

We investigate the Casimir effect as a probe of Lorentz symmetry violation for a real scalar field confined to a rectangular waveguide with Dirichlet boundary conditions. The field dynamics is governed by a Lorentz-violating extension of the Klein-Gordon theory involving a fixed background four-vector $u_μ$. Focusing on four representative configurations in which the background is aligned with the temporal direction or with one of the spatial axes of the cavity, we derive the modified mode spectra and the corresponding vacuum energies. We show that these configurations induce anisotropic modifications of the dispersion relations that depend explicitly on the orientation of the background vector relative to the cavity geometry, while still preserving mode separability. The resulting Casimir energy acquires characteristic direction-dependent corrections that encode the breaking of Lorentz symmetry, without altering the universal functional structure of the spectral kernel. Our analysis provides a controlled and transparent framework for isolating Lorentz-violating effects in confined geometries and highlights Casimir systems as sensitive probes of anisotropic physics and fundamental spacetime symmetries.

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arXiv2025

Vacuum Energy and Topological Mass in Interacting Elko and Scalar Field Theories

In this paper, we consider a four-dimensional system composed of a mass-dimension-one fermionic field, also known as Elko, interacting with a real scalar field. Our main objective is to analyze the Casimir effects associated with this system, assuming that both the Elko and scalar fields satisfy Dirichlet boundary conditions on two large parallel plates separated by a distance $L$. In this scenario, we calculate the vacuum energy density and its first-order correction in the coupling constants of the theory. Additionally, we consider the mass correction for each field separately, namely the topological mass that arises from the boundary conditions imposed on the fields and which also depends on the coupling constants. To develop this analysis, we use the mathematical formalism known as the effective potential, expressed as a path integral in quantum field theory.

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arXiv2025

Cylindrical boundary induced current in the cosmic string spacetime

In this paper we investigate the vacuum current associated with a charged bosonic field operator, induced by a cylindrical boundary in the idealized cosmic string spacetime. In this setup we assume that the cylindrical boundary is coaxial with the string, that by its turn carry a magnetic flux along its core. In order to develop this analysis, we calculate the positive frequency Wightman functions for both regions, inside and outside the boundary. Moreover, we assume that the bosonic field obeys the Robin boundary condition on the cylindrical shell. Using this approach, the analytical expressions for the vacuum bosonic currents are presented in the form of the sum of boundary-free and boundary-induced parts. Because the boundary-free contribution is very well established in literature, our focus here is in the boundary-dependent part. As we will see, our general results are presented in a cylindrically symmetric static structure. Some asymptotic behaviors for the boundary-induced vacuum currents are investigated in various limiting cases. In order to provide a better understanding of these currents, we provide some graphs exhibiting their behavior as function of the distance to the string's core, and on the intensity of the magnetic flux running along it. These plots also present how the parameter associated with the planar angle deficit interfere in the intensity of the corresponding current.

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arXiv2025

Vacuum energy density from a self-interacting scalar field in a Lorentz-violating Horava-Lifshitz model

In this paper we consider a massive self-interacting scalar quantum field in a Lorentz-violation scenario based on a Horava-Lifshitz model. Specifically, we investigate the vacuum energy density and its loop correction, up to first order in the self-interaction coupling constant, and also the topological mass generation. These quantities are also analyzed in the case where the field is massless. The scalar vacuum state is perturbed by the presence of two large parallel plates, placed at a distance L from each other, due to the imposition of Dirichlet boundary condition on the two plates. To perform this study, the effective potential approach in quantum field theory is applied.

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arXiv2024

Induced current in high-dimensional AdS bulk in the presence of a cosmic string and brane

In this paper we analyze the vacuum bosonic current associated with a massive charged scalar field propagating in a $(D+1)$-dimensional anti-de Sitter (AdS) bulk in the presence of an idealized carrying-magnetic-flux cosmic string and also a brane. We assume that the string is perpendicular to the brane which is parallel to the AdS boundary. The brane divides the space in two regions with different properties of vacuum states. We investigate the only non-vanishing azimuthal components of the induced currents in both regions. To develop this analysis we calculate first, for both regions, the positive frequency Wightman functions. These present contributions associated with the presence of a cosmic string only plus the other induced by the brane. In this talk we consider only the contributions induced by the brane.

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arXiv2024

Current density induced by a cosmic string in de Sitter spacetime in the presence of two flat boundaries

In this paper, we investigate the vacuum bosonic current density induced by a carrying-magnetic-flux cosmic string in a $(D+1)$-de Sitter spacetime considering the presence of two flat boundaries perpendicular to it. In this setup, the Robin boundary conditions are imposed on the scalar charged quantum field on the boundaries. The particular cases of Dirichlet and Neumann boundary conditions are studied separately. Due to the coupling of the quantum scalar field with the classical gauge field, corresponding to a magnetic flux running along the string's core, a nonzero vacuum expectation value for the current density operator along the azimuthal direction is induced. The two boundaries divide the space in three regions with different properties of the vacuum states. In this way, our main objective is to calculate the induced currents in these three regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Because the vacuum bosonic current in dS space has been investigated before, in this paper we consider only the contributions induced by the boundaries. We show that for each region the azimuthal current densities are odd functions of the magnetic flux along the string. To probe the correctness of our results, we take the particular cases and analyze some asymptotic limits of the parameters of the model. Also some graphs are presented exhibiting the behavior of the current with relevant physical parameter of the system.

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arXiv2024

Fermionic Casimir Energy in Horava-Lifshitz Scenario

In this work, we investigate the violation of Lorentz symmetry through the Casimir effect. The Casimir effect is one of the most intriguing aspects of modern physics, representing a macroscopic quantum-origin force between two neutral conducting surfaces, and it stands as a triumph of Quantum Field Theory. Here, we examine the Casimir effects associated with a massive fermionic quantum field confined in the region between two large and parallel plates within the Horava-Lifshitz framework of Lorentz symmetry violation. To calculate the Casimir energy and consequently the Casimir pressure, we impose a MIT bag boundary condition on two plates, compatible with the higher-order derivative term in the modified Dirac equation. Our results indicate a strong influence of Lorentz violation on the Casimir effect. We observe that the Casimir energy is affected, both in intensity and sign, potentially exhibiting repulsive or attractive force between the plates, depending on the critical exponent associated with the Horava-Lifshitz formalism.

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arXiv2024

Vacuum energy density for interacting real and complex scalar fields in a Lorentz symmetry violation scenario

In this paper the vacuum energy density and generation of topological mass are investigated for a system of a real and complex scalar fields interacting with each other. In addition to that, it is also included the quartic self-interaction for each one of the fields. The condition imposed on the real field is the periodic condition, while the complex field obey a quasi-periodic condition. The system is placed in a scenario where the CPT-even aether-type Lorentz symmetry violation takes place. We allow that the Lorentz violation affects the fields with different intensities. The vacuum energy density, its loop correction, and the topological mass are evaluated analytically. It is also discussed the possibility of different vacuum states and their corresponding stability requirements, which depends on the conditions imposed on the fields, the interaction coupling constants and also the Lorentz violation parameters. The formalism used here to perform this investigation is the effective potential one, which is written as a loop expansion via path integral in quantum field theory.

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arXiv2024

Finite temperature fermionic condensate and energy-momentum tensor in cosmic string spacetime

Here we analyze the expectation value of the fermionic condensate and the energy-momentum tensor associated with a massive charged fermionic quantum field with a nonzero chemical potential propagating in a magnetic-flux-carrying cosmic string in thermal equilibrium at finite temperature $T$. The expectation values of the fermionic condensate and the energy-momentum tensor are expressed as the sum of vacuum expectation values and the finite temperature contributions coming from the particles and antiparticles excitation. The thermal expectations values of the fermionic condensate and the energy-momentum tensor are even periodic functions of the magnetic flux with period being the quantum flux, and also even functions of the chemical potential. Because the analyses of vacuum expectation of the fermionic condensate and energy-momentum tensor have been developed in literature, here we are mainly interested in the investigation of the thermal corrections. In this way we explicitly study how these observable behaves in the limits of low and high temperatures, and also for points near the string. Besides the analytical discussions, we included some graphs that exhibit the behavior of these observable for different values of the physical parameters of the model.

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arXiv2024

Induced current by a cosmic string and a brane in high-dimensional AdS spacetime

In this paper we investigate the bosonic current induced by a brane and a magnetic flux running along the idealized cosmic string in a $(D+1)$-dimensional anti-de Sitter (AdS) background. We consider the brane is parallel to the AdS boundary and the cosmic string is orthogonal to them. Moreover, we assume that on the brane the charged bosonic field obeys the Robin boundary condition. The brane divides the space into two regions with different properties of the vacuum state. We show that the only nonzero component of the current density is along the azimuthal direction in both regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Both functions present a part associated with the AdS in presence of a cosmic string only, and the other part induced by the brane. In this paper we consider only the contributions induced by the brane. We show that in both regions the azimuthal current densities are odd functions of the magnetic flux along the string. Different analytic and numerical analysis are performed and an application of our results is provided for the Randall-Sundrum braneworld model with a single brane.

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arXiv2023

Vacuum effects induced by a plate in de Sitter spacetime in the presence of a cosmic string

In this paper we investigate the vacuum expectation values of the field squared and the energy-momentum tensor associated to a charged massive scalar quantum field in a $(1+D)$-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to do develop this analysis, we obtain the complete set of normalized positive-energy solution of the Klein-Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary induced vacuum polarization effects for both field squared and the energy-momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of cosmic string and boundary induce non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated.

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arXiv2023

Vacuum polarization induced by a cosmic string and a brane in AdS spacetime

In this paper we investigate the vacuum polarization effects associated to a charged quantum massive scalar field on a $(D+1)$-dimensional anti-de Sitter background induced by a magnetic-flux-carrying cosmic string in the braneworld model context. We consider the brane parallel to the anti-de Sitter boundary and the cosmic string orthogonal to them. Moreover, we assume that the field obeys the Robin boundary condition on the brane. Because the brane divides the space into two regions with different properties of the quantum vacuum, we calculate the vacuum expectation value (VEV) of the field squared and the energy-momentum tensor (EMT) in each region. To develop these analyses, we have constructed the positive frequency Wightman function for both regions. The latter is decomposed in a part associated with the anti-de Sitter bulk in the presence of a cosmic string only, and the other part induced by the brane. The vacuum polarization effects associated with the higher-dimensional anti-de Sitter bulk in the presence of cosmic string have been developed in the literature, and here we are mainly interested in the effects induced by the brane. We show that the VEVs of the field squared and the components of the EMT induced by the cosmic string are finite on the brane. Explicitly, we compare these observables with the corresponding ones induced by the brane only, and show that near the brane the contribution induced by the latter is larger than the one induced by the string; however, for points distant from the brane the situation is reversed. Moreover, some asymptotic expressions for the VEV of the field squared and EMT are provided for specific limiting cases of the physical parameters of the model. Also, an application of our results is given for a cosmic string in the $Z_2$-symmetric Randall-Sundrum braneworld model with a single brane.

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arXiv2023

Bosonic Casimir effect in an aether-like Lorentz-violating scenario with higher order derivatives

In this paper we investigate the bosonic Casimir effect in a Lorentz-violating symmetry scenario. The theoretical model adopted consists of a real massive scalar quantum field confined in a region between two large parallel plates, having its dynamics governed by a modified Klein-Gordon equation that presents a Lorentz symmetry breaking term. In this context we admit that the quantum field obeys specific boundary conditions on the plates. The Lorentz-violating symmetry is implemented by the presence of an arbitrary constant space-like vector in a CPT-even aether-like approach, considering a direct coupling between this vector with the derivative of the field in higher order. The modification on the Klein-Gordon equation produces important corrections on the Casimir energy and pressure. Thus, we show that these corrections strongly depend on the order of the higher derivative term and the specific direction of the constant vector, as well as the boundary conditions considered.

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