A THOUGHTFUL STUDY OF LORENTZ TRANSFORMATIONS BY CLIFFORD ALGEBRAS

Abstract

We give a thoughtful presentation of proper orthocronous Lorentz transformations using the space-time (ℝ1,3) and the Pauli (ℝ3,0) algebras. We present in a closed finite form, a generic [Formula: see text] written as the exponential of elements of the associated Lie Algebra, together with a physical interpretation of the parameters. We call the result obtained the master equation and it is used to study several important topics of Special Relativity, e.g. exact product of two boosts and the Thomas precession. We also derive other results necessary for a dynamic interpretation of Lorentz transformations.