Discrete Space-time and Lorentz Transformations

Canadian mathematical bulletin

Christian Pommerenke²  Gerd Jensen¹ 

[1] Sensburger Allee 22 a , D--14055 Berlin;Institut für Mathematik , Technische Universität, D--10623 Berlin

关键词: Lorentz transformation;    integer lattice;    Gaussian integers;   

DOI  :  10.4153/CMB-2015-066-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Alfred Schild has established conditions that Lorentz transformations map world-vectors $(ct,x,y,z)$ with integer coordinates onto vectors of the same kind. The problem was dealt with in the context of tensor and spinor calculus. Due to Schild's number-theoretic arguments, the subject is alsointeresting when isolated from its physical background. The paper of Schild is not easy to understand. Therefore we first present a streamlined version of his proof which is based on the use of null vectors. Then we present a purely algebraic proof that is somewhat shorter. Both proofs rely on the propertiesof Gaussian integers.

【 授权许可】

Unknown