Vacuum decay and fermion total reflection by the Klein step

TL;DR

This paper re-examines Klein tunneling in quantum field theory, showing that fermions are totally reflected with vacuum decay and pair production in the Klein energy range, providing a new perspective on the phenomenon.

Contribution

It introduces a quantum field theory approach to Klein tunneling, revealing vacuum decay and pair production as key features of fermion scattering at a potential step.

Findings

Fermions are totally reflected in the Klein energy range.

Vacuum decay occurs, producing fermion-antifermion pairs.

Two asymptotic vacua are related by a similarity transformation.

Abstract

The so-called Klein tunneling is re-examined within the framework of quantum field theory, but from a different point of view on the asymptotic states. We treat it as a one-dimensional scattering process of a fermion incident to a step potential and introduce asymptotic operators as appropriate $t = \pm \infty$ limits of the field operator responsible for the process. For the so-called Klein energy range, two asymptotic vacua naturally emerge which are defined as states annihilated by the asymptotic annihilation operators. They are related by a similarity transformation, which entails a vacuum decay and yields a vacuum decay constant. When a fermion with incident energy in the Klein region is injected to the step, it is shown to be reflected with probability one, accompanied by fermion--anti-fermion pairs that are vacuum decay products.