Unstable vacuum and fermion total reflection by the Klein step

Abstract

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 = ±∞ 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 an unstable vacuum. 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.