On some discrete subgroups of the Lorentz group

TL;DR

This paper investigates specific discrete subgroups of the Lorentz group using Fedorov's parametrization, revealing their structure and classification based on fixed points and vector types, with implications for understanding Lorentz symmetries.

Contribution

It identifies and classifies discrete subgroups of the Lorentz group using complex vector-parameter parametrization, distinguishing between fixed point and non-fixed point subgroups.

Findings

Non-fixed point subgroups are contained in boosts along a spatial direction.

Discrete subgroups of non-isotropic vectors are subgroups of SO(1,1)×E(1,1).

Subgroups related to time-like and space-like vectors are contained in SO(1,1).

Abstract

Some discrete subgroups of the Lorentz group are found using Fedorov's parametrization by means of complex vector-parameter. It is shown that the discrete subgroup of the Lorentz group, which have not fixed points, are contained in boosts along a spatial direction for time-like and space-like vectors and are discrete subgroups of the group SO(1,1), whereas discrete subgroups of isotropic vector are subgroups of SO(1,1)\times E(1,1).