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On the Structure of the Schild Group in Relativity Theory
Published online by Cambridge University Press: 20 November 2018
Abstract
Alfred Schild has established conditions that Lorentz transformationsmap world-vectors $(ct,x,y,z)$ with integer coordinates onto vectors of the same kind. These transformations are called integral Lorentz transformations.
This paper contains supplements to our earlier work with a new focus on group theory. To relate the results to the familiar matrix group nomenclature, we associate Lorentz transformations with matrices in $\text{SL}(2,\mathbb{C})$. We consider the lattice of subgroups of the group originated in Schild's paper and obtain generating sets for the full group and its subgroups.
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- Copyright © Canadian Mathematical Society 2017