A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

Vitória, R. L. L.; Belich, H.; Bakke, K.

doi:10.1140/epjp/i2017-11305-4

Cited by 60 publications

(80 citation statements)

References 71 publications

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“…1 show that for small values of ω, E n → ±M for any n. Eq. (47) shows that E n,m depends on n and the spectrum of energy is discrete. For s = −1, the expression for E n,m contains all the terms of Eq.…”

Section: The Dirac Oscillator In Cosmic String Backgroundmentioning

confidence: 99%

“…For s = −1, the expression for E n,m contains all the terms of Eq. (47) and depends on all its parameters, including m, a and α. The positive values of the energy spectrum with s = −1 is displayed as a function of α (with M = 1, m = 1/2, a = 0.1 and ω = 1, for n = 1 and 2, in Fig.…”

Section: The Dirac Oscillator In Cosmic String Backgroundmentioning

confidence: 99%

“…Some studies of relativistic oscillators are in Refs. [40][41][42][43][44][45][46][47].In this work, we examine the relativistic quantum dynamics of Dirac oscillator on the curved spacetime of a rotating cosmic string. From the corresponding Dirac equation, we analyze the influence of the topological defect on the equation of motion, the energy spectrum and the wave-functions.…”

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confidence: 99%

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The Dirac oscillator in a spinning cosmic string spacetime

2019

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We examine the effects of gravitational fields produced by topological defects on a Dirac field and a Dirac oscillator in a spinning cosmic string spacetime. We obtain the eigenfunctions and the energy levels of the relativistic field in that background and consider the effect of various parameters, such as the frequency of the rotating frame, the oscillator's frequency, the string density and other quantum numbers. DIRAC EQUATION IN THE COSMIC STRING SPACETIMEbetween quarks as well as the confining part of the phenomenological Cornell potential), the Dirac oscillator and related models have been applied in many other contexts as well, such as quantum optics [7][8][9], supersymmetry [5, 10, 11], nuclear reactions [12], the hadronic spectrum (with the two-body Dirac oscillator) [13,14], the Clifford algebra [15,16], noncommutative space [17,18], thermodynamic properties [19], Lie algebras [20], supersymmetric (non-relativistic) quantum mechanics [21], the supersymmetric path-integral formalism [22], chiral phase transitions in presence of a constant magnetic field [8], the relativistic Landau levels in presence of external magnetic field [23], the Aharonov-Bohm effect [24], and condensed matter physics phenomena and graphene [25]. Similar studies for the Duffin-Kemmer-Petiau (DKP) oscillator, which is analogous to the Dirac oscillator for spinless and spin-one particles, are in Refs. [26,27]. Finally, let us mention many studies of the Dirac oscillator with topological defects and cosmic string spacetimes in Refs. [28][29][30][31][32][33][34] and analogous investigations for scalar fields in Refs. [35][36][37][38][39]. Some studies of relativistic oscillators are in Refs. [40][41][42][43][44][45][46][47].In this work, we examine the relativistic quantum dynamics of Dirac oscillator on the curved spacetime of a rotating cosmic string. From the corresponding Dirac equation, we analyze the influence of the topological defect on the equation of motion, the energy spectrum and the wave-functions. An analogous study for the Klein-Gordon equation is in Ref. [49]. In Sec. 2, we write down the covariant Dirac equation without oscillator in a spinning cosmic string spacetime, and find its wave-functions and energy eigenvalues. In Sec. 3, we present the covariant Dirac oscillator in the same spacetime and obtain the wave-functions and energy spectrum. We present concluding remarks in Sec. 4.

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Section: The Dirac Oscillator In Cosmic String Backgroundmentioning

confidence: 99%

Section: The Dirac Oscillator In Cosmic String Backgroundmentioning

confidence: 99%

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confidence: 99%

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The Dirac oscillator in a spinning cosmic string spacetime

2019

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“…On the other hand, the matrices of the parity-odd sector are defined as ( ) = −( ) = ( ) 0 and have no symmetry). Thereby, the Klein-Gordon equation can be written in the following form [18,33,36]…”

Section: Relativistic Effectsmentioning

confidence: 99%

“…Equation (8) , which means that ℎ( ) is written as a power series expansion around the origin [36,48]. Thereby, we substitute ℎ( ) = ∑ ∞ =0…”

Section: Relativistic Effectsmentioning

confidence: 99%

Coulomb-Type Interaction under Lorentz Symmetry Breaking Effects

Vitória

Belich

Bakke

2017

Advances in High Energy Physics

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Based on models of confinement of quarks, we analyse a relativistic scalar particle subject to a scalar potential proportional to the inverse of the radial distance and under the effects of the violation of the Lorentz symmetry. We show that the effects of the Lorentz symmetry breaking can induce a harmonic-type potential. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background of the violation of the Lorentz symmetry on the relativistic energy levels.

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