Real Dirac Theory

The Dirac theory is completely reformulated in terms of Spacetime Algebra, a real Clifford Algebra characterizing the geometrical properties of spacetime. This eliminates redundancy in the conventional matrix formulation and reveals a hidden geometric structure in the theory. Among other things, it reveals that complex numbers in the Dirac equation have a kinematical interpretation, with the unit imaginary identified as the generator of rotations in a spacelike plane representing the direction of electron spin. Thus, spin and complex numbers are shown to be inextricably related in the Dirac Theory. This leads to a new version of the zitterbewegung, wherein local circular motion of the electron is directly associated with the phase factor of the wave function. In consequence, the electron spin and magnetic moment can be attributed to the zitterbewegung, and many other features of quantum mechanics can be explained as zitterbewegung resonances.