华东师范大学学报(自然科学版) ›› 2016, Vol. 2016 ›› Issue (3): 76-83.doi: 2016.03.009

• 物理学 • 上一篇    下一篇

SIM(2)引力规范理论

吴奕暐, 薛迅   

  1. 华东师范大学~~物理系，上海 200241
  • 收稿日期:2015-05-06 出版日期:2016-05-25 发布日期:2016-09-22
  • 通讯作者: 薛 迅, 男, 副教授, 硕士生导师, 研究方向为洛伦兹破缺、等效引力理论、与暗物质有关的超越标准模型理论. E-mail: xxue@phy.ecnu.edu.cn
  • 作者简介:吴奕暐, 男，硕士研究生,研究方向为洛伦兹破缺、等效引力理论、与暗物质有关的超越标准模型理论.

SIM(2) gravitational gauge theory

 WU  Yi-Wei, XUE  Xun   

  • Received:2015-05-06 Online:2016-05-25 Published:2016-09-22

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摘要： 基于宇宙微波背景辐射~(Cosmic Microwave Background Radiation, CMB)~的各向异性观测结果和马赫原理,假设了洛伦兹~(Lorentz)~对称性从大于星系尺度开始破缺,并基于这个动机以~SIM(2)~规范理论为例, 诠释了所谓的``暗物质效应'',意即天文观测上对牛顿－爱因斯坦(Newton-Einstein)引力理论预言的偏离,可以由小尺度上~Lorentz~对称性的破缺在大尺度上的累积呈展出来.分析了~SIM(2)~规范理论, 在场运动方程之外得到了~8~个约束方程,并且将独立~contorsion~分量个数也约化到了~8~个.得到了~contorsion~是非平庸的,并且即使在没有物质分布的区域也会贡献一个等效的能－动张量分布. 最后,分析了在弱场近似下的度规柱对称解, 分析了此解的性质.

关键词: SIM(2)群, 洛伦兹破缺, 引力规范理论, contorsion

Abstract: Based on the anisotropies of CMB (Cosmic Microwave Background Radiation, CMB) on the large scale and Mach's principle,this paper proposed that the Lorentz invariance is violated from the length scale of galaxy. SIM(2) gauge theory was taken as an example of such motivation to illustrate the so called dark matter effect,the deviation of astronomical observation from Newton-Einstein prediction, which can be emerged from the accumulated Lorentz violation effect on the short scale. SIM(2) gauge theory was analyzed and 8 additional constrain equations were obtained in addition to the equation of motion, while the independent components of contorsion were also reduced to 8. It can lead us to the conclusion that the contorsion is non-trivial and can contribute an
effective energy-momentum distribution even in the region devoid of matter. Finally, the cylindrical symmetrized solution of metric under weak field expansion was given and its property was analyzed.

Key words: SIM(2) group, Lorentz breaking, gravitational gauge theory, contorsion

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