Reformulation of the Dirac Theory of the Electron

It is shown that when the Dirac theory is formulated in the formalism of the dynamical group O(4, 2), there is no need to invoke the hole theory or the notion of backward motion in time to describe antiparticles. A single irreducible representation of O(4, 2) is used and the discrete operators $P$, $C$ become inner automorphisms of the group. The most general linear minimal parity-violating equation generalizing the Dirac equation is shown to lead to two possible distinct mass values.