Quantization of charged fields in the presence of critical potential steps

Abstract

QED with strong external backgrounds that can create particles from the vacuum is well developed for the so-called t-electric potential steps, which are time-dependent external electric fields that are switched on and off at some time instants. However, there exist many physically interesting situations where external backgrounds do not switch off at the time infinity. E.g., these are timeindependent nonuniform electric fields that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x-electric potential steps for charged particles. They can also create particles from the vacuum, the Klein paradox being closely related to this process. Approaches elaborated for treating quantum effects in the t-electric potential steps are not directly applicable to the x-electric potential steps and their generalization for x-electric potential steps was not sufficiently developed. We believe that the present work represents a consistent solution of the latter problem. We have considered a canonical quantization of the Dirac and scalar fields with x-electric potential step and have found in-and out-creation and annihilation operators that allow one to have particle interpretation of the physical system under consideration. To identify in-and out-operators we have performed a detailed mathematical and physical analysis of solutions of the relativistic wave equations with an x-electric potential step with subsequent QFT analysis of correctness of such an identification. We elaborated a nonperturbative (in the external field) technique that allows one to calculate all characteristics of zero-order processes, such, for example, scattering, reflection, and electron-positron pair creation, without radiation corrections, and also 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 of x-electric potential steps, namely, to the Sauter potential and to the Klein step.

Particle creation by peak electric field

“…Thus, using some results of the latter work, below we summarize the structure of solutions for each interval and unify it in a single presentation. To this aim we introduce new variables η j , 12) in place of t and represent the scalar functions ϕ n (t) as 13) where the subscript j distinguishes quantities associated to the intervals I ( j = 1) and II ( j = 2), respectively. Then the functionsφ j (η j ) satisfy the confluent hypergeometric equation [41],…”

“…In most interesting cases, when the semiclassical approximation is not applicable, the most convincing consideration of the effect is formulated in the framework of quantum field theory, in particular, in the framework of QED, see Refs. [4,5,7,12,13] and is based on the existence of exact solutions of the Dirac equation with the corresponding external field. Until now, only few exactly solvable cases are known for either time-dependent homogeneous or constant inhomogeneous electric fields.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13]. To be observable, the effect needs very strong electric fields in magnitudes compared with the Schwinger critical field.…”

Electron-positron pair production in external electric fields varying both in space and time

“…This approach is formulated in detail in Ref. [7] (for the case of static space-dependent electric fields the quantization procedure is different [18]). The Dirac equation in the presence of an external field contains the minimal coupling terms:…”

“…[1][2][3] where a static potential step was considered (see also Refs. [18,19] and references therein).…”