重力场中Dirac方程的非相对论近似  

Non-relativistic approximation of Dirac equation in gravity field

作　　者：郭光杰 GUO Guangjie(School of Physics and Electronic Engineering, Xingtai University, Xingtai 054001, China;Xingtai Key Laboratory for Research and Application of Robot Intelligent Detection and Sorting Technology, Xingtai University, Xingtai 054001, China)

机构地区：[1]邢台学院物理与电子工程学院,河北邢台054001 [2]邢台学院邢台市机器人智能检测与分拣技术研究与应用重点实验室,河北邢台054001

出　　处：《湘潭大学学报（自然科学版）》2022年第3期65-71,共7页Journal of Xiangtan University(Natural Science Edition)

基　　金：邢台市青年科技人才计划项目(2018ZZ033);邢台学院校级课题(XTXY13YB079)。

摘　　要：中子在重力场中波长的变化,提供了一个观察引力量子效应准确无误的例证,为理解引力的本质提供了一个窗口.严格来说,引力场中的中子应该用弯曲时空中的狄拉克方程描述.但是,用薛定谔方程描述的非相对论量子理论确能很好地解释中子引力干涉实验.本文旨在研究这两种理论描述的自洽性.首先,介绍了中子的引力干涉实验和非相对论量子理论描述;其次,给出了Schwarzschild度规下的狄拉克方程;最后,推导出了Schwarzschild度规下狄拉克方程的非相对论近似.研究发现,在低能且弱引力场近似下,弯曲时空的狄拉克方程可以自然地过渡到非相对论薛定谔方程,引力的效应得到牛顿引力势和对动能的修正,但该动能修正项和引力势相比可忽略不计.The wavelength of neutrons in the gravity field displays a clear and definite quantum effect of gravity,which provides us a window to see the nature of gravity.Literally,the dynamics of a neutron in a gravity field should be described by the Curved Time-Space Dirac Equation(CTSDE).However,the neutrons’gravitationally induced quantum interference can be explained well by the non-relativistic quantum theory.This paper is aimed at studying the consistency of these two theories.Firstly,the experiment of neutrons’gravitationally induced quantum interference and its description of non-relativistic quantum theory are introduced briefly.Secondly,the Dirac Equation with Schwarzschild Metric is given.Lastly,the non-relativistic approximation of Dirac Equation with Schwarzschild Metric is derived.It is found that under the low-energy and weak-gravity approximation,the CTSDE degenerates subsequently to the Non-relativistic Schrodinger Equation,and the gravity effect is embodied in Newton’s gravitational potential and a correction for kinetic energy.Under the weak-gravity approximation this kinetic energy correction can be neglected in comparison with the gravitational potential.

关 键 词：弯曲时空中的Dirac方程 SCHWARZSCHILD度规 重力势 

分 类 号：O412.1[理学—理论物理]