arXiv subjects

L. H. C. Borges

Publications and source records attributed to L. H. C. Borges.

At least 19 recordsLinked to original sources

arXiv2026

External Sources in Pseudo-Quantum Electrodynamics

In this letter, we investigate the interaction between stationary point-like external sources within the framework of Pseudo-Quantum Electrodynamics (PQED). Besides ordinary electric charges, we consider configurations involving Dirac points and generalized topological sources. For the configurations analyzed, we compute the corresponding interaction energies, forces, torques, and electromagnetic field configurations. Furthermore, we compare the results obtained in PQED with those arising in ordinary planar Maxwell electrodynamics, showing that the nonlocal character of PQED gives rise to physical effects with no counterpart in the conventional local planar theory. In particular, our results show that topological sources induce intrinsically anisotropic and non-central interactions, leading to the emergence of nontrivial torques between the interacting objects. The directional character of these interactions suggests possible applications in the effective description of topological defects and anisotropic phenomena in planar condensed matter systems.

hep-th↗

arXiv2026

Point-Like Charges and Dirichlet Boundary Conditions in a Nonlocal Scalar Field Theory

In this paper, we investigate novel classical non-local effects in scalar field theory arising from the presence of external sources and a material boundary. Specifically, we consider a model in which the standard Klein-Gordon field theory is modified by a non-local term. First, we analyze the interaction between stationary field sources modeled as point-like scalar charges. In specific configurations, the resulting interparticle potential reduces to the Cornell form. Then, we examine the model in the presence of a Dirichlet plane, computing both the scalar field propagator and the interaction force between the Dirichlet plane and a point-like scalar charge. Additionally, we demonstrate the failure of the image method in this non-local context and compare our results with those obtained in non-local electrodynamics and in the standard Klein-Gordon field theory.

hep-th↗

arXiv2025

Generalized Neumann boundary condition for the scalar field

In this paper, we explore the Klein-Gordon field theory in $(D+1)$ dimensions in the presence of a $(D-1)$-dimensional hyperplanar $δ$-like potential that couples quadratically to the field derivatives. This model effectively generalizes the Neumann boundary condition for the scalar field on the plane, as it reduces to this condition in an appropriate limit of the coupling parameter. Specifically, we calculate the modifications to the Feynman propagator induced by the planar potential and analyze the interaction energy between a stationary point-like source and the potential, obtaining a general and exact expression. We demonstrate that, under certain conditions relating the field mass and the coupling constant to the external potential, the vacuum state becomes unstable, giving rise to a pair-creation phenomenon that resembles the Schwinger effect in quantum electrodynamics.

hep-th↗

arXiv2025

The role of scalar current coupling along surfaces

In this paper we propose a coupling between the complex scalar field and an external Dirac delta-like planar potential. The coupling is achieved through the Klein-Gordon current normal to the plane where the potential is concentrated. The results are obtained exactly and exhibit many peculiarities. We show that a complex scalar charge does not interact with the potential, but the potential modifies the interaction between two scalar charges if they are placed on opposite sides of the planar potential. When the coupling constant between the potential and the field goes to infinity, the classical field solutions satisfy a kind of MIT boundary conditions along the plane where the potential is concentrated.

hep-th↗

arXiv2024

On the five-dimensional non-extremal Reissner-Nordström black hole: Retractions and scalar quasibound states

In this paper, we examine the role played by topology, and some specific boundary conditions as well, on the physics of a higher-dimensional black hole. We analyze the line element of a five-dimensional non-extremal Reissner-Nordström black hole to obtain a new family of subspaces that are types of strong retractions and deformations, and then we extend these results to higher dimensions in order to deduce the relationship between various types of transformations. We also study the scalar field perturbations in the background under consideration and obtain an analytical expression for the quasibound state frequencies by using the Vieira-Bezerra-Kokkotas approach, which uses the polynomial conditions of the general Heun functions, and then we discuss the stability of the system and present the radial eigenfunctions. Our main goal is to discuss the physical meaning of these mathematical applications in such higher-dimensional effective metric.

gr-qc↗

arXiv2024

Material boundaries in Carroll-Field-Jackiw Lorentz-violating electrodynamics

This paper investigates certain aspects of the CPT-odd photon sector of the minimal Standard Model Extension (SME) in the presence of a perfectly conducting plate (perfect mirror). The considered sector is described by Carroll-Field-Jackiw (CFJ) electrodynamics, where Lorentz violation is due to the presence of a single background vector denoted as $\left(k_{AF}\right)^μ$, which we treat perturbatively up to second order. Specifically, we derive the modified propagator for the electromagnetic field due to the presence of the perfect mirror, and we study the corresponding interaction between the mirror and a stationary point-like charge. Our results reveal that when the charge is positioned near the mirror, a spontaneous torque emerges, which is a unique effect of Lorentz symmetry breaking. Additionally, we demonstrate that the image method for this theory is applicable when the background vector has only the component perpendicular to the mirror.

hep-th↗

arXiv2024

Field sources in a planar anisotropic CPT-odd gauge model

In the present paper we study some new classical Lorentz violating effects in planar electrodynamics due to the presence of stationary point-like field sources. Starting from the Carroll-Field-Jackiw model defined in (3+1) dimensions, which belongs to the electromagnetic CPT-odd sector of the Standard Model Extension (SME), we apply the dimensional reduction procedure obtaining a (2+1)-dimensional model that encompasses an electromagnetic sector composed of the Maxwell-Chern-Simons electrodynamics, a pure scalar sector described by a massless Klein-Gordon field, and a mixed sector where the background vector mediates contributions involving both the scalar and the gauge fields. For all the sectors of this planar theory, we explore some physical phenomena that arise from the interactions between external sources. Specifically, we obtain perturbative effects up to second order in the background vector related to the presence of both electric and scalar planar charges and Dirac points.

hep-th↗

arXiv2022

Semi-transparent boundaries in CPT-even Lorentz violating electrodynamics

Some aspects of the nonbirefringent CPT-even gauge sector of the Standard Model Extension (SME), in the vicinity of a semi-transparent mirror, are investigated in this paper. We first consider a model where the Lorentz symmetry breaking is caused by a single background vector $v^μ$, and we obtain perturbative results up to second order in $v^μ$. Specifically, we compute the modified propagator for the gauge field due to the presence of the mirror and we analyze the corresponding interaction between the mirror and a stationary point-like charge. We show that when the charge is placed in the vicinity of the mirror, a spontaneous torque emerges, which is a new effect with no counterpart in Maxwell electrodynamics. We also compare these results with the corresponding ones obtained for the Lorentz violating scalar field theory. As expected, in the limiting case of perfect mirrors, we recover the interaction found via the image method. Finally, we discuss how we can extend these results for a more general Lorentz violating background.

hep-th↗

arXiv2022

External sources in a minimal and nonminimal CPT-odd Lorentz violating Maxwell electrodynamics

This paper is devoted to the study of interactions between stationary electromagnetic sources for the minimal and nonminimal CPT-odd photon sector of the Standard Model Extension (SME), where we search mainly for physical phenomena not present in the Maxwell electrodynamics. First we consider the minimal CPT-odd sector, where the Lorentz violation is caused by the Carroll-Field-Jackiw (CFJ) term, namely $\simε^{μναβ}\left(k_{AF}\right)_μA_νF_{αβ}$, and we treat the Lorentz breaking parameter $\left(k_{AF}\right)^μ$ perturbatively up to second order. We consider effects due to the presence of point-like charges, Dirac strings and point-like dipoles. In special, we calculate the electromagnetic field produced outside the string and investigate the so called Aharonov-Bohm bound states in Lorentz violation context. After, we consider a model where the Lorentz violation is generated by the higher-derivative version of the CFJ model, namely $\simε^{μναβ}V_μA_ν\Box F_{αβ}$, which is a dimension five term of the CPT-odd sector of the nonminimal SME. For this higher-derivative model, we obtain effects up to second order in $V^μ$ related to the presence of point-like charges and a steady current line. We use overestimated constrains for the Lorentz violation parameters in order to investigate the physical relevance of some results found in atomic systems. We also make an overestimate for the background vectors using experimental data from the atomic electric field.

hep-th↗

arXiv2022

Features of planar Lee-Wick electrodynamics

In this letter we study some aspects of the planar Lee-Wick electrodynamics near a perfectly conducting line (unidimensional mirror). Specifically, the modified Lee-wick propagator due to the presence of a conducting line is calculated, and the interaction between the mirror and the point-like charge is investigated. It is shown that the behavior of this interaction is very different from the one already known for the $(3+1)$-dimensional Lee-Wick electrodynamics, where we have a planar mirror. It is also shown that the image method is not valid in planar Lee-Wick electrodynamics and the dimensional reduction yields a stronger taming of divergences.

hep-th↗

arXiv2022

Higher order derivatives extension of Maxwell-Chern-Simons electrodynamics in the presence of field sources and material boundaries

In this paper we consider some new classical effects obtained for a planar electrodynamics with the presence of a higher order derivatives term. The model can be interpreted as a kind of extension for the $3d$ Maxwell-Chern-Simons electrodynamics with higher order derivatives. We consider setups with stationary field sources describing point-like charges and Dirac points. We also investigate this model with the presence of a conducting line (in $3d$ dimensions, it is the equivalent of a conducting plate in $4d$ dimensions). In this case we calculate the propagator for the gauge field and the interaction force between the conducting line and a point-like charge, as well as the force between the conducting line and a Dirac point, the source for vortex field solutions. It is shown that the image method is not valid in any case. We also compare the obtained results along the paper with the corresponding ones obtained with the standard Maxwell-Chern-Simons electrodynamics [1].

hep-th↗

arXiv2022

Magnetoelectric boundary simulated by a Chern-Simons-like model

In this work we study some physical phenomena that emerge in the vicinity of a magnetoelectric boundary. For simplicity, we restrict to the case of a planar boundary described by a coupling between the gauge field with a planar external Chern-Simons-like potential. The results are obtained exactly. We compute the correction undergone by the photon propagator due to the presence of the Chern-Simons coupling and we investigate the interaction between a stationary point-like charge and the magnetoelectric boundary. In the limit of a perfect mirror, where the coupling constant between the field and the potential diverges, we recover the image method. For a non perfect mirror, we show that we have an attenuated image charge and, in addition, an image magnetic monopole whose field strength does not exhibit the presence of the undesirable and artificial divergences introduced by Dirac strings. We also study the interaction between the plate and a quantum particle with spin. In this case we have a kind of charge-magnetic dipole interaction due to the magnetoelectric properties of the plate.

hep-th↗

arXiv2020

Dirichlet boundary condition for the Lee-Wick-like scalar model

Lee-Wick-like scalar model near a Dirichlet plate is considered in this work. The modified propagator for the scalar field due to the presence of a Dirichlet boundary is computed, and the interaction between the plate and a point-like scalar charge is analysed. The non-validity of the image method is investigated and the results are compared with the corresponding ones obtained for the Lee-Wick gauge field and for the standard Klein-Gordon field.

hep-th↗

arXiv2020

New point-like sources and a conducting surface in Maxwell-Chern-Simons electrodynamics

We investigate some aspects of the Maxwell-Chern-Simons electrodynamics focusing on physical effects produced by the presence of stationary sources and a perfectly conducting plate (mirror). Specifically, in addition to point charges, we propose two new types of point-like sources called topological source and Dirac point, and we also consider physical effects in various configurations that involve them. We show that the Dirac point is the source of the vortex field configurations. The propagator of the gauge field due to the presence of a conducting plate and the interaction forces between the plate and point-like sources are computed. It is shown that the image method is valid for the point-like charges as well as for Dirac points. For the topological source we show that the image method is not valid and the symmetry of spatial refection on the mirror is broken. In all setups considered, it is shown that the topological source leads to the emergence of torques.

hep-th↗

arXiv2020

Mirrors and field sources in a Lorentz-violating scalar field theory

In this paper we consider different classical effects in a model for a scalar field incorporating Lorentz symmetry breaking due to the presence of a single background vector v^μ coupled to its derivative. We perform an investigation of the interaction energy between stationary steady sources concentrated along parallel branes with an arbitrary number of dimensions, and derive from this study some physical consequences. For the case of the scalar dipole we show the emergence of a nontrivial torque, which is distinctive sign of the Lorentz violation. We also investigate a similar model in the presence of a semi-transparent mirror. For a general relative orientation between the mirror and the v^μ, we are able to perform calculations perturbatively in v^μ up to second order. We also find results without recourse to approximations for two special cases, that of the mirror and v^μ being parallel or perpendicular to each other. For all these configurations, the propagator for the scalar field and the interaction force between the mirror and a point-like field source are computed. It is shown that the image method is valid in our model for the Dirichlet's boundary condition, and we argue that this is a non-trivial result. We also show the emergence of a torque on the mirror depending on its orientation with respect to the Lorentz violating background. This is a new effect with no counterpart in theories with Lorentz symmetry in the presence of mirrors.

hep-th↗

arXiv2019

The point-charge self-energy in a nonminimal Lorentz violating Maxwell Electrodynamics

In this letter we study the self-energy of a point-like charge for the electromagnetic field in a non minimal Lorentz symmetry breaking scenario in a $n+1$ dimensional space time. We consider two variations of a model where the Lorentz violation is caused by a background vector $d^ν$ that appears in a higher derivative interaction. We restrict our attention to the case where $d^μ$ is a time-like background vector, namely $d^{2}=d^μd_μ>0$, and we verify that the classical self-energy is finite for any odd spatial dimension $n$ and diverges for even $n$. We also make some comments regarding obstacles in the quantization of the proposed model.

hep-th↗

arXiv2019

Higher order derivative operators as quantum corrections

In this paper we propose a non-minimal, and ghost free, coupling between the gauge field and the fermionic one from which we obtain, perturbatively, terms with higher order derivatives as quantum corrections to the photon effective action in the low energy regime. We calculate the one-loop effective action of the photon field and show that, in addition to the Euler-Heisenberg terms, the well known Lee-Wick term, $\sim F_{μν}\partial_α\partial^αF^{μν}$, arises in low energy regime as a quantum correction from the model. We also obtain the electron self energy in leading order.

hep-th↗

arXiv2019

Field sources in a CPT-even Lorentz-violation Maxwell electrodynamics

This paper is dedicated to the study of interactions between external sources for the electromagnetic field in a model which exhibits Lorentz symmetry breaking. We investigate such interactions in the CPT-even photon sector of the Standard Model Extension (SME), where the Lorentz symmetry breaking is caused by a background tensor $K_{(F)αβστ}$. Since the background tensor is very tiny, we treat it perturbatively up to first order and we focus on physical phenomena which have no counterpart in Maxwell electrodynamics. We consider effects related to field sources describing point-like charges, straight line currents and Dirac strings. We also investigate the so called Aharonov-Bohm bound states in a Lorentz-symmetry breaking scenario. We use atomic experimental data to verify if we could impose upper bounds to the Lorentz-symmetry breaking parameters involved. We also use some overestimated constrains for the Lorentz-symmetry breaking parameters in order to investigate if the obtained results could be relevant for condensed matter systems.

hep-th↗