The Dirac Equation from the Perspective of Quaternionic Analysis

Abstract The Dirac equation is mapped to a first order differential equation for complex quaternionic functions to benefit from potential theory and quaternionic analysis. This method provides solutions which do not depend on particular matrix representations for Clifford algebras. We additionally deduce zero-mode solutions for the Dirac–Weyl equation, when non-vanishing vector potentials are presupposed.