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E. O. Silva

Publications and source records attributed to E. O. Silva.

At least 19 recordsLinked to original sources
arXiv2014

On the $κ$-Dirac Oscillator revisited

This Letter is based on the $κ$-Dirac equation, derived from the $κ$-Poincaré-Hopf algebra. It is shown that the $κ$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, $\mathbf{p}\to\mathbf{p}-imωβ\mathbf{r}$, in the $κ$-Dirac equation, one obtains the $κ$-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where $\varepsilon=0$, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.

hep-th↗
arXiv2013

On the spin-1/2 Aharonov-Bohm problem in conical space: bound states, scattering and helicity nonconservation

In this work the bound state and scattering problems for a spin-1/2 particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and $S$ matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio $g$ are discussed. Also, as an application, we consider the spin-1/2 Aharonov-Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator.

quant-ph↗
arXiv2013

A CPT-even Lorentz-violating nonminimal coupling between fermions and photons

We propose a CPT-even and Lorentz-violating dimension-five nonminimal coupling between fermionic and gauge fields, involving the CPT-even and Lorentz-violating gauge tensor of the Standard-Model Extension. This nonminimal coupling modifies the nonrelativistic regime of Dirac particles, inducing new effects such as an electric-Zeeman-like spectrum splitting and an anomalous-like contribution to the electron magnetic moment. These new effects allow to constrain the magnitude of this nonminimal coupling in 1 part in $10^{16}.$

hep-th↗
arXiv2013

On the Aharonov-Casher scattering in a CPT-odd Lorentz-violating background

The effects of a Lorentz symmetry violating background vector on the Aharonov-Casher scattering in the nonrelativistic limit is considered. By using the self-adjoint extension method we found that there is an additional scattering for any value of the self-adjoint extension parameter and non-zero energy bound states for negative values of this parameter. Expressions for the energy bound states, phase-shift and the scattering matrix are explicitly determined in terms of the self-adjoint extension parameter. The expression obtained for the scattering amplitude reveals that the helicity is not conserved in this scenario.

hep-th↗
arXiv2013

On Aharonov-Casher bound states

In this work bound states for the Aharonov-Casher problem are considered. According to Hagen's work on the exact equivalence between spin-1/2 Aharonov-Bohm and Aharonov-Casher effects, is known that the $\boldsymbol{\nabla}\cdot\mathbf{E}$ term cannot be neglected in the Hamiltonian if the spin of particle is considered. This term leads to the existence of a singular potential at the origin. By modeling the problem by boundary conditions at the origin which arises by the self-adjoint extension of the Hamiltonian, we derive for the first time an expression for the bound state energy of the Aharonov-Casher problem. As an application, we consider the Aharonov-Casher plus a two-dimensional harmonic oscillator. We derive the expression for the harmonic oscillator energies and compare it with the expression obtained in the case without singularity. At the end, an approach for determination of the self-adjoint extension parameter is given. In our approach, the parameter is obtained essentially in terms of physics of the problem.

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arXiv2013

Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background

The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter.

hep-th↗
arXiv2012

A new CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation

In this work, we propose a CPT-even and Lorentz-violating dimension-five nonminimal coupling between fermionic and gauge fields, involving the CTP-even and Lorentz-violating gauge tensor of the SME. This nonminimal coupling modifies the Dirac equation, whose nonrelativistic regime is governed by a Hamiltonian which induces new effects, such as an electric-Zeeman-like spectrum splitting and an anomalous-like contribution to the electron magnetic moment, between others. Some of these new effects allows to constrain the magnitude of this nonminimal coupling in 1 part in 10^16.

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arXiv2012

Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem

In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the $κ$-Poincaré-Hopf algebra. We consider the nonrelativistic limit of the $κ$-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter $\varepsilon$. By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the $S$-matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using a recently developed general regularization prescription [Phys. Rev. D. \textbf{85}, 041701(R) (2012)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.

hep-th↗
arXiv2012

Nonrelativistic quantum dynamics on a cone with and without a constraining potential

In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we compare and discuss the results stemming from two different approaches. In the first one, it is assumed that the charge carriers are bound to the surface by a constraining potential, while the second one is based on the Klein-Gordon type equation on surfaces, without the constraining potential. The main difference between both theories is the presence/absence of a potential which contains the mean curvature of a given surface. This fact changes the dependence of the bound states on the angular momentum $l$. Moreover, there are bound states that are absent in the Klein-Gordon theory, which instead appear in the Schrödinger one.

quant-ph↗
arXiv2012

He-McKellar-Wilkens effect and Scalar Aharonov-Bohm effect for a neutral particle based on the Lorentz symmetry violation

In this contribution, we discuss the He-McKellar-Wilkens effect and the Scalar Aharonov-Bohm effect for neutral particles based on the Lorentz symmetry violation background, by showing that the background of the Lorentz symmetry violation yields abelian quantum phases for a neutral particle. We also study the nonrelativistic bound states for a neutral particle interacting with a Coulomb-like potential based on the Lorentz symmetry violation background given by a fixed vector field parallel to the radial direction.

hep-th↗
arXiv2012

Quantum harmonic oscillator for dipoles

In this work we investigate which radial field configuration yields bound states for neutral particles showing non-zero magnetic and electric dipole moments. The main result is that, in contrast with previous works, the Landau analog levels only exist if these radial magnetic and electric external fields are proportional to the third power of distance, not proportional to the distance. We derive the wave functions and the energy levels in the context of commutative and non-commutative quantum mechanics. We also show that, in the case of non-commutative phase space, these harmonic oscillator like spectrum do exist even if there is no external radial magnetic and electric fields. They are only consequence of the non-commutativity in the momenta.

hep-th↗
arXiv2012

Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space

We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the δ-function singularity coming from the Zeeman spin interaction with the magnetic flux tube is solved through the self-adjoint extension method. Using two different approaches already known in the literature, both based on the self-adjoint extension method, we obtain the self-adjoint extension parameter to the bound state and scattering scenarios in terms of the physics of the problem. It is shown that such a parameter is the same for both situations. The method is general and is suitable for any quantum system with a singular Hamiltonian that has bound and scattering states.

quant-ph↗
arXiv2011

Aharonov-Bohm-Casher Problem with a nonminimal Lorentz-violating coupling

The Aharonov-Bohm-Casher problem is examined for a charged particle describing a circular path in presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field. It were evaluated the particle eigenenergies, showing that the LV background is able to lift the original degenerescence in the absence of magnetic field and even for a neutral particle. The Aharonov-Casher phase is used to impose an upper bound on the background magnitude. A similar analysis is accomplished in a space endowed with a topological defect, revealing that both the disclination parameter and the LV background are able to modify the particle eigenenergies. We also analyze the particular case where the particle interacts harmonically with the topological defect and the LV background, with similar results.

hep-th↗
arXiv2008

On the noncommutative fields method in the three-dimensional Yang-Mills theory

We apply the noncommutative fields method to the three-dimensional non-Abelian gauge theory. We find that, first, implementing the noncommutativity between the canonical momenta implies in generation of the non-Abelian Chern-Simons term, second, if one introduces the noncommutativity between the field operators, the higher derivative terms would arise.

hep-th↗
arXiv2008

On duality of the noncommutative Maxwell-Chern-Simons theory

We study the possibility of establishing the dual equivalence between the noncommutative Maxwell-Chern-Simons theory and the noncommutative self-dual theory. It turns to be that whereas in the commutative case the Maxwell-Chern-Simons theory can be mapped into the sum of the self-dual theory and the Chern-Simons theory, in the noncommutative case such a mapping is possible only for the theory with the modified Maxwell term.

hep-th↗
arXiv2007

Anomaly cancellation in three-dimensional noncommutative gauge theories

The anomaly found by Callan and Harvey is shown to be cancelled in a three-dimensional noncommutative gauge theory coupled to a fermion with a mass function depending on one spatial coordinate (domain wall mass). This evaluation has been done for the fermion in the fundamental and adjoint representations of the gauge group in the limit of small noncommutativity $θ$ parameter.

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