We compare the predictions of the single-particle Dirac equation with quantum field theory for an electron subjected to a space and time dependent field. We demonstrate analytically and numerically that a transition into the negative-energy subspace predicted by the single-particle Dirac equation is directly associated with the degree of suppression of pair-production as described by quantum field theory. We show that the portion of the mathematical wave function that populates the negative-energy states corresponds to the difference between the positron spatial density for systems with and without an electron initially present.
Krekora, P; Su, Q; and Grobe, Rainer, "Transitions into the negative-energy Dirac continuum" (2004). Faculty publications – Physics. 28.