Dirac equation with space contributions embedded in a quantum-corrected gravitational field

IF 3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
M. Baradaran , L.M. Nieto , S. Zarrinkamar
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引用次数: 0

Abstract

The Dirac equation is considered with the recently proposed generalized gravitational interaction (Kepler or Coulomb), which includes post-Newtonian (relativistic) and quantum corrections to the classical potential. The general idea in choosing the metric is that the spacetime contributions are contained in an external potential or in an electromagnetic potential which can be considered as a good basis for future studies of quantum physics in space. The forms considered for the scalar potential and the so-called vector (magnetic) potential, can be viewed as the multipole expansion of these terms and therefore the approach includes a simultaneous study of multipole expansions to both fields. We also comment on the special case of the problem with merely a relativistic correction in terms of Heun functions. The impossibility of solving our equation for the quantum-corrected Coulomb terms using known exact or quasi-exact nonperturbative analytical techniques is discussed, and finally the Bethe-ansatz approach is proposed to overcome this challenging problem.
在量子修正引力场中嵌入空间贡献的狄拉克方程
狄拉克方程与最近提出的广义引力相互作用(开普勒或库仑)一起考虑,其中包括对经典势的后牛顿(相对论)和量子修正。选择度规的一般思想是,时空贡献包含在外部势或电磁势中,这可以被认为是未来空间量子物理研究的良好基础。考虑的标量势和所谓的矢量(磁)势的形式可以看作是这些项的多极展开,因此该方法包括对两个场的多极展开的同时研究。我们还评论了仅用Heun函数作相对论性修正的问题的特殊情况。讨论了使用已知的精确或准精确非微扰解析技术求解量子校正库仑项方程的不可能性,最后提出了Bethe-ansatz方法来克服这一具有挑战性的问题。
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来源期刊
Annals of Physics
Annals of Physics 物理-物理:综合
CiteScore
5.30
自引率
3.30%
发文量
211
审稿时长
47 days
期刊介绍: Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.
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