Light-Cone Expansion of the Dirac Sea to First Order in the External Potential

摘要

In relativistic quantum mechanics, the problem of the unphysical negative - energy solutions of the Dirac equation is solved by the conception that all negative- energy states are occupied in the vacuum forming the so-called Dirac sea . In [1], the Dirac sea was consimcted for the Dirac equation with general interaction in terms of a formal power series in the extemal potential. In the present paper, we turn our attention to a single Feynman diagram of this perturbation expansion. More pre- cisely, we will analyze the contribution to first order in the potential and derive explicit formulas for the Dirac sea in position space. Since this analysis does not require a detailed knowledge of the perturbation expansion for the Dirac sea, we can make this paper selfconsistent by giving a brief introduction to the mathe- matical problem.