Observables, operators, and complex numbers in the Dirac theory

Abstract

The geometrical formulation of the Dirac theory with spacetime algebra is shown to be equivalent to the usual matrix formalism. Imaginary numbers in the Dirac theory are shown to be related to the spin tensor. The relation of observables to operators and the wavefunction is analyzed in detail and compared with some purportedly general principles of quantum mechanics. An exact formulation of Larmor and Thomas precessions in the Dirac theory is given for the first time. Finally, some basic relations among local observables in the nonrelativistic limit are determined.