The Lorentz operator revisited

Abstract

Some kinematical aspects of the decomposition of the product of two pure Lorentz operators into the product of a third pure Lorentz operator and a pure rotation are discussed. It is shown that a triangle can be associated with such a decomposition and the properties of such a triangle are compared with those of a triangle in the more conventional hyperbolic geometry. The lack of uniqueness in this decomposition is discussed. Finally, a Lorentz operator containing six independent parameters is expressed in terms of the initial and final vectors of the corresponding Lorentz transformation.