Pair production from the vacuum by a weakly inhomogeneous space-dependent electric potential

Abstract

There exists a clear physical motivation for theoretical studies of the vacuum instability related to the production of electron-positron pairs from a vacuum due to strong external electric fields. Various nonperturbative (with respect to the external fields) calculation methods were developed. Some of these methods are based on possible exact solutions of the Dirac equation. Unfortunately, there are only few cases when such solutions are known. Recently, an approximate but still nonperturbative approach to treat the vacuum instability caused by slowly varying t-electric potential steps (time dependent external fields that vanish as |t| → ∞), which does not depend on the existence of the corresponding exact solutions, was formulated in Ref. [S. P. Gavrilov, D. M. Gitman, Phys. Rev. D 95, 076013 (2017)]. Here, we present an approximate calculation method to treat nonperturbatively the vacuum instability in arbitrary weakly inhomogeneous x-electric potential steps (timeindependent electric fields of a constant direction that are concentrated in restricted space areas, which means that the fields vanish as |x| → ∞) in the absence of the corresponding exact solutions. Defining the weakly inhomogeneous regime in general terms, we demonstrate the universal character of the vacuum instability. This universality is associated with a large density of states excited from the vacuum by the electric field. Such a density appears in our approach as a large parameter. We derive universal representations for the total number and current density of the created particles. Relations of these representations with a locally constant field approximation for Schwinger's effective action are found.Center for Extreme Light Studies (XCELS), is slowly approaching the critical field strengths for observable pair production (see Ref.[13] for a review). Thus, there exists a clear physical motivation for theoretical studies of the vacuum instability. Firstly, it seems necessary to us to mention theoretical works devoted to various nonperturbative (with respect to the external field) calculation methods. Some of these methods are formulated for time-dependent external fields that vanish as |t| → ∞ (for t-electric potential steps in what follows) and are based on possible exact solutions of the Dirac equation; see, e.g., [6,[14][15][16][17]. Some of the methods are based on the analysis of the Schwinger effective action (see [18] for a review). The so-called derivative expansion approximation method, being applied to the Schwinger effective action, allows one to treat effectively arbitrary slowly varying in time strong fields [19,20]. We note that the locally constant field approximation (LCFA), which is to limit oneself to leading contributions of the derivative expansion of the effective action, allows for reliable results for electromagnetic fields of arbitrary strength; see, for example, Refs. [21,22]. An alternative approach to treat slowly varying t-electric potential steps, which does not depend on the existence of the corresponding exa...

Regularization, renormalization and consistency conditions in QED with x-electric potential steps

“…[20] for details. Using the developed approach [20] we succeeded to calculate global effects (global quantities) of zero order with respect to the radiative interaction, such that the vacuum-to-vacuum transition amplitude c v , the mean differential and the total numbers of created particles, and so on for the number of x-steps (step between two capacitor plates, Sauter, Klein, and exponential steps); see [27,[29][30][31]. However, a number of important technical and principal questions still need to be answered.…”

“…It should be noted that, recently, there was proposed a new formulation of locally constant field approximations (LCFAs) in QED with x-steps, which does not rely on the Heisenberg-Euler action [31] (a similar approximation was formulated in QED with t-steps slowly varying with time [37]). As part of this formulation, we have constructed universal approximate representations for the total number and current density of the created particles in arbitrary weakly inhomogeneous x-steps.…”

In- and out-states of scalar particles confined between two capacitor plates

“…In this case, the field and the leading contributions to the vacuum mean values can be considered as macroscopic ones. However, this -constant electric field is weakly inhomogeneous, the corresponding Klein zone is extensive, so that all the universal properties of the vacuum instability described by Gavrilov, Gitman and Shishmarev (2019) hold true. The -constant field in the limit is a kind of a regularisation for a constant uniform electric field.…”

“…This technique was effectively used to describe particle creation effect in the Sauter field of the form , in a constant electric field between two capacitor plates separated by a distance (the so-called -constant electric field), and in exponential time-independent electric steps, where the corresponding exact solutions were available (see Gavrilov, Gitman 2016a;2016b;Gavrilov, Gitman, Shishmarev 2017). These exactly solvable models make it possible to develop a new approximate calculation method to non-perturbatively treat the vacuum instability in arbitrary weakly-inhomogeneous x-electric potential steps (Gavrilov, Gitman, Shishmarev 2019). Note that the corresponding limiting case of a constant uniform electric field shares many similarities with the case of the de Sitter background (see Anderson, Mottola 2014;Akhmedov, Popov 2015 and references therein).…”

Particle creation in the context of the emergent universe

“…Recently, the particle creation problem under the influence of electromagnetic and/or gravitational fields was studied in [19][20][21][22][23][24][25][26][27]. Also, more recently, the Schwinger effect by an SU(2) gauge field during inflation for scalar particles and fermions was calculated in [28] and [29,30].…”