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QFT approaches elaborated for treating quantum effects in time-dependentexternal electric fields are not directly applicable to time-independentnonuniform electric fields that are given by a step potential and theirgeneralization for the such potentials was not sufficiently developed. Suchfields can also create particles from the vacuum, the Klein paradox beingclosely related to this process. We believe that the present work presents aconsistent solution of the latter problem. Quantizing the Dirac and scalarfields with time independent backgrounds, we have found in- and out-creationand annihilation operators that allow one to have particle interpretation ofthe physical system under consideration. To justify the proposedidentification, we have performed a detailed mathematical and physical analysisof solutions of the corresponding relativistic wave equations with a subsequentQFT analysis. We elaborated a nonperturbative technique that allows one tocalculate all characteristics of zero-order processes such scattering,reflection, and electron-positron pair creation, and to calculate Feynmandiagrams that describe all characteristics of processes with interactionbetween the in-, out-particles and photons. These diagrams have formally theusual form, but contain special propagators. Expressions for these propagatorsin terms of in- and out-solutions are presented. We apply the elaboratedapproach to two popular exactly solvable cases: to the Sauter potential and tothe Klein step.

Quantization of charged fields in the presence of critical potential steps