The Klein paradox as a many particle problem

Abstract

In this paper we give a mathematically rigorous analysis of the Klein paradox in the many-particle formulation of the Dirac theory. This paradox was meant as an example demonstrating the negative energy problems of the single particle Dirac equation. However, we show that this problem does not disappear in the second quantized version of the Dirac theory. It corresponds with a situation which cannot be described properly within the framework of a field theory with an external potential.