Group Structure of an Extended Lorentz Group

Abstract

In a previous paper we extended the Lorentz group to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The group is particularly useful for developing general linear wave equations beyond spin 1/2 systems. In this paper we develop explicit group properties of this extended Lorentz group to obtain group parameters that will be useful for physical calculations for systems which might manifest the group properties. This group is a subgroup of an extended Poincare group, whose structure will be developed in a subsequent paper.