Two-Body Dirac Theory

Abstract

Zitterbewegung is the quiver motion discovered by Schroedinger in his 1930 solution of the time-dependent Dirac equation for a free electron. The origin of Zitterbewegung is the interference between positive-energy and negative-energy states. Zitterbewegung is predicted to exist for both free and bound electrons provided one discards Dirac’s hypothesis, known as hole theory, whereby positive-energy electrons are forbidden from occupying negative-energy states such that Zitterbewegung is suppressed. The positive-energy spectra of states is identical whether one uses hole theory, in which Zitterbewegung is suppressed (restricted solution), or whether one uses the solution in which electrons are not restricted from simultaneously occupying both positive-energy and negative-energy states such that Zitterbewegung is not suppressed (unrestricted solution). Thus both the restricted and unrestricted solutions are confirmed by spectroscopic experimental observation such that new experiments are motivated to discriminate between the restricted and unrestricted solutions. Hole theory (the restricted solution) is used to interpret the experimental observation of electron-positron pair creation and annihilation. In this paper we look for pair states in the negative-energy region of the Dirac spectrum in order to understand if the unrestricted solution, which correctly predicts the positive-energy spectrum and Zitterbewegung, is also correct in the description of pair creation and annihilation.