广义相对论中的狄拉克方程和3+1形式

IF 2.8 4区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS
Miguel Alcubierre
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引用次数: 0

摘要

我对广义相对论中的狄拉克方程进行了回顾。虽然狄拉克方程对弯曲时空的推广是众所周知的,但它通常不是研究经典广义相对论的人所知道的标准技术工具包的一部分。最近,人们对研究爱因斯坦-狄拉克方程组的解产生了新的兴趣,特别是在所谓的“狄拉克星”的背景下。受此启发,我在此对广义相对论中的狄拉克方程进行了回顾,从闵可夫斯基时空开始,然后考虑洛伦兹群和四分体形式,以便将该方程推广到弯曲时空的情况。我还推导了广义相对论3+1形式的狄拉克方程及其相关的应力-能量张量的形式,这对于研究狄拉克场在动态时空中的演化是有用的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Dirac equation in general relativity and the 3+1 formalism

I present a review of the Dirac equation in general relativity. Although the generalization of the Dirac equation to a curved spacetime is well known, it is not usually part of the standard toolkit of techniques known to people working on classical general relativity. Recently, there has been some renewed interest in studying solutions of the Einstein–Dirac system of equations, particularly in the context of the so-called “Dirac stars”. Motivated by this, here I present a review of the Dirac equation in general relativity, starting from Minkowski spacetime, and then considering the Lorentz group and the tetrad formalism in order to generalize this equation to the case of a curved spacetime. I also derive the form of the Dirac equation and its associated stress–energy tensor for the case of the 3+1 formalism of general relativity, which can be useful for the study of the evolution of the Dirac field in a dynamical spacetime.

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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.
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