Lorentz Group, Poincaré Group, and Minkowski Geometry

Abstract

As a consequence of the Principle of Relativity, the set P of transformations between inertial systems has a certain mathematical structure: composing two transformations from P gives a transformation from P again, and for each transformation from P there is a unique inverse in P. The set P therefore forms a group where the group multiplication law is given by the composition of transformations.