On a purely geometric approach to the Dirac matter field and its quantum properties

Abstract: We consider the most general axial torsion completion of gravity with electrodynamics for $\frac{1}{2}$-spin spinors in an $8$-dimensional representation of the Dirac matter field: this theory will allow to define antimatter as matter with all quantum numbers reversed, where also the sign of the mass beside that of the charge is inverted: we shall see that matter and antimatter solutions of the Dirac field equations coincide with the known ones with respect to all observables, that despite the inversion of the sign of the mass term only positive-mass states are present and only positive-energy densities are given; the present and the common approach will be compared, and some experimental implications will be discussed.