A quaternion formulation of the Dirac equation

Abstract

In this thesis the formalisms of quaternions and biquaternions have been employed to reformulate Dirac's relativistic wave equation and to investigate claims concerning elegance, intuitiveness and new physical results of such a formulation. In this fashion, an elegant formulation of the Dirac equation in terms of biquaternions was found. After this, reproduction of some well-known physical results like plane wave solutions and the nonrelativistic approximation were achieved. It must be admitted, however, that there seems to be no reason to believe that a quaternion or biquaternion formulation of the Dirac equation contains any additional physics and the purpose of getting used to a different formalism than the usual may be questioned as it does not seem to have deepened the understanding of the Dirac equation.