Geodesic
Discrete Space-time and Lorentz Transformations
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 123-135

Voir la notice de l'article provenant de la source Cambridge University Press

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
DOI : 10.4153/CMB-2015-066-4
Mots-clés : 22E43, 20H99, 83A05, Lorentz transformation, integer lattice, Gaussian integers 
Jensen, Gerd; Pommerenke, Christian. Discrete Space-time and Lorentz Transformations. Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 123-135. doi: 10.4153/CMB-2015-066-4
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