Extension Theorem and Representations

Abstract

An extension theorem prescribing a method for constructing the (n + 1)‐dimensional Lorentz group O(n, 1) from the n‐dimensional inhomogeneous rotation group, proved earlier, has been recapitulated and some comments on the theorem are made. The prescription is used to construct the unitary irreducible representations of the Lorentz groups O(2, 1), O(3, 1), and O(4, 1), and it is found that only a limited number of representations are allowed.