The Real Dirac Equation

Dirac’s leaping insight that the normalized anticommutator of the gamma matrices have to equal the relativistic timespace signature was decisive for the successful formulation of his famous Equation. The Dirac matrices represent ‘some internal degrees of freedom of the electron’ and are the same in all Lorentz frames. Therefore, the link to the timespace signature of special relativity constitutes a postulate of Dirac’s theory. I show in the present contribution that all the properties of the Dirac electron / positron follow from the direct quantization of the relativistic 4-momentum vector – preconceived ‘internal degrees of freedom’, matrices and imposed signature unneeded.

By choosing to accomodate the quantization postulate in a real 5D vector space, it becomes possible to generate a Clifford algebra isomorphic to that of the Dirac matrices with all the complex structure arising solely from the vectorial quantities. The fifth dimension relates to handedness / reflection that in the proposed scheme becomes as fundamental as the four dimensions of spacetime. The expanded vector space is therefore named spacetime-reflection, STR. After a short introduction to STR I will sketch the quantization procedure leading to the STR Dirac Equation, STR DE. I will focus on the physical content of the STR DE as illustrated by its manifest covariance, symmetries, conserved currents, spin and nonrelativistic approximation.