A Superalgebraic Form of the Dirac Equation

Abstract

A spinor theory with automatic second quantization and no need for normalizing operators is constructed, based on a superalgebraic representation of spinors and Dirac matrices. The creation and annihilation operators of spinors are constructed using integrals of Grassmann variable densities in the momentum space and derivatives with respect to them. Formulas for superalgebraic bilinear covariants, and fermionic Lagrangian, and Noether currents are derived.