An Interpretation of Dirac's Theory of the Electron

Toyoki Koga

William C. Daywitt

David Hestenes

By a new method, the Dirac electron theory is completely reexpressed as a set of conservation laws and constitutive relations for local observables, describing the local distribution and flow of mechanical quantities. The coupling of the electromagnetic field to the electron is shown to be determined by the definitions of the observables rather than by the Dirac equation. Planck's constant appears in the equations only in connection with the electron spin. The equations are most readily interpreted by assuming that the electron is a structureless point charge, the spin and magnetic moment arising from the dynamics of electron motion.

Bernd Thaller

Considers the Dirac equation with external electromagnetic fields and gives a careful formulation of the Stuckelberg-Feynman interpretation. This electron-positron theory may be applied whenever electron and positron states can be separated, which is possible for a wide class of time-independent potentials vanishing at infinity. One then may introduce a system of observables with a position operator X(t) which is free of Zitterbewegung and yields the usual relativistic connection between momentum and velocity. The Stuckelberg-Feynman interpretation is usually associated with a scattering theory (propagator formalism), which differs from the one of a one-particle interpretation (formalism imitating non-relativistic techniques). For the above-mentioned potentials there is a simple relationship between these physically different formalisms. There are, however, more general potentials for which the Stuckelberg-Feynman interpretation may still be applied asymptotically. With the help of Klein's paradox the authors show that the Dirac equation may then have unphysical solutions not conserving the total charge.

P. A. M. Dirac

Wanda Hanus