Quantization of charged fields in the presence of critical potential steps

TL;DR

This paper develops a quantum field theory approach for charged fields in static, nonuniform electric fields with step potentials, enabling analysis of particle creation and scattering with a new nonperturbative technique.

Contribution

It introduces a consistent quantization method for charged fields in step potentials, including a nonperturbative calculation technique for particle processes and Feynman diagrams with special propagators.

Findings

Derived in- and out-operators for particle interpretation.

Calculated scattering, reflection, and pair creation characteristics.

Applied method to Sauter potential and Klein step cases.

Abstract

QFT approaches elaborated for treating quantum effects in time-dependent external electric fields are not directly applicable to time-independent nonuniform electric fields that are given by a step potential and their generalization for the such potentials was not sufficiently developed. Such fields can also create particles from the vacuum, the Klein paradox being closely related to this process. We believe that the present work presents a consistent solution of the latter problem. Quantizing the Dirac and scalar fields with time independent backgrounds, we have found in- and out-creation and annihilation operators that allow one to have particle interpretation of the physical system under consideration. To justify the proposed identification, we have performed a detailed mathematical and physical analysis of solutions of the corresponding relativistic wave equations with a subsequent QFT analysis. We elaborated a nonperturbative technique that allows one to calculate all characteristics of zero-order processes such scattering, reflection, and electron-positron pair creation, and to calculate Feynman diagrams that describe all characteristics of processes with interaction between the in-, out-particles and photons. These diagrams have formally the usual form, but contain special propagators. Expressions for these propagators in terms of in- and out-solutions are presented. We apply the elaborated approach to two popular exactly solvable cases: to the Sauter potential and to the Klein step.