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Discrete Space-time and Lorentz Transformations

Published online by Cambridge University Press:  20 November 2018

Gerd Jensen  and
Christian Pommerenke
Gerd Jensen
Affiliation:
Sensburger Allee zz a, D–14055 Berlin e-mail: cg.jensen@arcor.de
Christian Pommerenke
Affiliation:
Institut für Mathematik, Technische Universität, D–10623 Berlin e-mail: pommeren@math.tu-berlin.de
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Abstract

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Alfred Schild established conditions where Lorentz transformations map world-vectors $\left( ct,\,x,\,y,\,z \right)$ 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 also interesting when isolated from its physical background.

Schild’s paper 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 properties of Gaussian integers

Keywords

22E4320H9983A05Lorentz transformationinteger latticeGaussian integers
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 1 , 01 March 2016 , pp. 123 - 135
Copyright
Copyright © Canadian Mathematical Society 2016

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