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The relating geometry in Special Relativity
Zheng-chen Liang #,Bao-guo Hao *
Guang Dong Olympic School, The Affiliated High School of SCNU, Guangzhou 510630
*Correspondence author
#Submitted by
Subject:
Funding: Education Foundation of the Affiliated High School of SCNU for YA 2016 in Mathematics, South Final（No.16112303）
Opened online:26 May 2017
Accepted by: none
Citation: Zheng-chen Liang,Bao-guo Hao.The relating geometry in Special Relativity[OL]. [26 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4728382
 
 
Based on the abundant properties of Minkowski spacetime $mathcal{M}$ in Special Relativity, here we create a geometric structure in fiber-bundle language which relates the tangent bundle $mathcal{TM}$ to Cartan subalgebra $mathfrak{h}$ of the gauge Lie algebra $mathfrak{g}$ of connected compact Lie group $G$. In the relating geometry, the structural group of principal bundle $P$ is the quotient group $G_Sigma=G/H$ by a maximum torus subgroup $H$, while the positive-definite Cartan subalgebra $mathfrak{h}$ with an Exponential Map to $H$ holds the bundle of $mathfrak{q}_x=mathcal{T}_xmathcal{M}oplusmathfrak{h}$. If the bundle of $mathfrak{q}_x$ is trivial over $mathcal{M}$, a relater $t_lpha^{ eta}$ for the Maurer-Cartan connection 1-form of $mathcal{M}$ can be solved when $ ext{dim} H=4$. The geometry has an instant application to classical observations on massive particles. It provides the modification with a Variable-Speed-of-Light (VSL) derived from the Clifford values in $mathfrak{q}_x$ and the associative bundle $mathfrak{E}_x$.
Keywords:local differential geometry; fiber bundle; Cartan decomposition; connection form; relater
 
 
 

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