Iterants and the Dirac Equation

Abstract

Abstract This paper introduces the concept of iterant algebra and applies it to the formation of basic Clifford algebras including a reconstruction of the complex numbers in terms of a formalization of temporal process. Iterant algebra is shown to include all of matrix algebra and applications are given to a representation of the su(3) Lie algebra for the Standard Model and to the construction of the Dirac Equation. This construction of the Dirac Equation makes it clear how solutions arise from nilpotent elements in the Clifford algebra and how Fermion algebra and the algebra of Majorana Fermions emerges in this context. The paper ends with a formulation of the original Majorana Dirac Equation in terms of Clifford algebra in the context of iterants.