Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime

IF 2.8 4区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS
R. R. S. Oliveira
{"title":"Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime","authors":"R. R. S. Oliveira","doi":"10.1007/s10714-025-03447-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we determine the relativistic bound-state solutions for the charged (DO) Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime in <span>\\((2+1)\\)</span>-dimensions, where such solutions are given by the two-component normalizable Dirac spinor and by the relativistic energy spectrum. To analytically solve our problem, we consider two approximations, where the first is that the cosmological constant is very small (conical approximation), and the second is that the linear velocity of the rotating frame is much less than the speed of light (slow rotation regime). After solving a second-order differential equation, we obtain a generalized Laguerre equation, whose solutions are the generalized Laguerre polynomials. Consequently, we obtain the energy spectrum, which is quantized in terms of the radial and total magnetic quantum numbers <i>n</i> and <span>\\(m_j\\)</span>, and depends on the angular frequency <span>\\(\\omega \\)</span> (describes the DO), cyclotron frequency <span>\\(\\omega _c\\)</span> (describes the external magnetic field), angular velocity <span>\\(\\Omega \\)</span> (describes the rotating frame), spin parameter <i>s</i> (describes the “spin”), spinorial parameter <i>u</i> (describes the components of the spinor), effective rest mass <span>\\(m_{eff}\\)</span> (describes the rest mass modified by the spin-rotation coupling), and on a real parameter <span>\\(\\sigma \\)</span> and cosmological constant <span>\\(\\Lambda \\)</span> (describes the Bonnor-Melvin-Lambda spacetime). In particular, we note that this spectrum is asymmetrical (due to <span>\\(\\Omega \\)</span>) and has its degeneracy broken (due to <span>\\(\\sigma \\)</span> and <span>\\(\\Lambda \\)</span>). Besides, we also graphically analyze the behavior of the spectrum and of the probability density as a function of the parameters of the system for different values of <i>n</i> and <span>\\(m_j\\)</span>.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 7","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-025-03447-5","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, we determine the relativistic bound-state solutions for the charged (DO) Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime in \((2+1)\)-dimensions, where such solutions are given by the two-component normalizable Dirac spinor and by the relativistic energy spectrum. To analytically solve our problem, we consider two approximations, where the first is that the cosmological constant is very small (conical approximation), and the second is that the linear velocity of the rotating frame is much less than the speed of light (slow rotation regime). After solving a second-order differential equation, we obtain a generalized Laguerre equation, whose solutions are the generalized Laguerre polynomials. Consequently, we obtain the energy spectrum, which is quantized in terms of the radial and total magnetic quantum numbers n and \(m_j\), and depends on the angular frequency \(\omega \) (describes the DO), cyclotron frequency \(\omega _c\) (describes the external magnetic field), angular velocity \(\Omega \) (describes the rotating frame), spin parameter s (describes the “spin”), spinorial parameter u (describes the components of the spinor), effective rest mass \(m_{eff}\) (describes the rest mass modified by the spin-rotation coupling), and on a real parameter \(\sigma \) and cosmological constant \(\Lambda \) (describes the Bonnor-Melvin-Lambda spacetime). In particular, we note that this spectrum is asymmetrical (due to \(\Omega \)) and has its degeneracy broken (due to \(\sigma \) and \(\Lambda \)). Besides, we also graphically analyze the behavior of the spectrum and of the probability density as a function of the parameters of the system for different values of n and \(m_j\).

Bonnor-Melvin-Lambda时空中旋转框架中带电狄拉克振子的束缚态解
本文确定了(2+1)(2+1)维Bonnor-Melvin-Lambda时空中旋转坐标系中带电(DO)狄拉克振子的相对论束缚态解,其中这些解由双分量可归一化狄拉克旋量和相对论能谱给出。为了解析地解决我们的问题,我们考虑两种近似,第一种是宇宙学常数非常小(圆锥近似),第二种是旋转框架的线速度远小于光速(慢旋转状态)。在求解二阶微分方程后,得到了广义拉盖尔方程,其解为广义拉盖尔多项式。因此,我们得到了用径向和总磁量子数n和mjm_j量子化的能谱,它取决于角频率ω \omega(描述DO)、回旋频率ωc \omega _c(描述外部磁场)、角速度Ω \Omega(描述旋转框架)、自旋参数s(描述“自旋”)、旋量参数u(描述旋量的组成)、有效静止质量{meffm_eff}(描述自旋-旋转耦合修正后的静止质量),以及实参数σ \sigma和宇宙学常数Λ \Lambda(描述bonor - melvin - lambda时空)。特别地,我们注意到这个谱是不对称的(由于Ω \Omega),并且它的简并性被打破了(由于σ \sigma和Λ \Lambda)。此外,我们还图形化地分析了不同n和mjm_j值下谱和概率密度作为系统参数的函数的行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
General Relativity and Gravitation
General Relativity and Gravitation 物理-天文与天体物理
CiteScore
4.60
自引率
3.60%
发文量
136
审稿时长
3 months
期刊介绍: General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation. It welcomes in particular original articles on the following topics of current research: Analytical general relativity, including its interface with geometrical analysis Numerical relativity Theoretical and observational cosmology Relativistic astrophysics Gravitational waves: data analysis, astrophysical sources and detector science Extensions of general relativity Supergravity Gravitational aspects of string theory and its extensions Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations Quantum field theory in curved spacetime Non-commutative geometry and gravitation Experimental gravity, in particular tests of general relativity The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信