Spinor-Quaternion Analysis in Relativity Theory

Abstract

Not long after Dirac discovered that to maintain the Schrödinger form of quantum mechanics, in a way that would be consistent with the symmetry requirements of special relativity theory, it is necessary to extend from the complex scalar wave function formulation to a spinor formulation, Einstein and Mayer [4] asked the following question: “Is it possible that the appearance of the ‘spinor variable’ in Dirac’s electron equation was in fact necessitated by the imposition of relativistic covariance, and does not depend on the quantum mechanical nature of the description per se?” To answer this question, these authors investigated the minimum-dimensional representations of the symmetry group of special relativity theory — the Poincaré group.