Violation of vacuum stability by inverse square electric fields

Abstract

In the framework of QED with a strong background, we study particle creation (the Schwinger effect) by a time-dependent inverse square electric field. To this end corresponding exact in-and out-solutions of the Dirac and Klein-Gordon equations are found. We calculate the vacuum-to-vacuum probability and differential and total mean numbers of pairs created from the vacuum. For electric fields varying slowly in time, we present detailed calculations of the Schwinger effect and discuss possible asymptotic regimes. The obtained results are consistent with universal estimates of the particle creation effect by electric fields in the locally constant field approximation. Differential and total quantities corresponding to asymmetrical configurations are also discussed in detail. Finally, the inverse square electric field is used to imitate switching on and off processes. Then the case under consideration is compared with the one where an exponential electric field is used to imitate switching on and off processes.

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

“…(1.4). This assumption seems quite natural, as much of this behavior is observed for results obtained in exactly solvable cases with t-steps [21][22][23][24][25][26] and numerical calculations; see, e.g. [26].…”

“…However, both fast switching-on and -off produce electronpositron pairs with quantum numbers of the tiny range of kinetic energy and one can neglect these contributions to any total characteristics of particle creation, which are determined by the sum over all kinetic energies, if the time T satisfies Eq. (1.4) [21][22][23][24][25][26]. These total characteristics are, for example, the vacuum-to-vacuum transition probability, pairproduction rate, and fluxes of charge and energy of created particles.…”

Vacuum instability in a constant inhomogeneous electric field: a new example of exact nonperturbative calculations

“…In the case of the t-steps, these are particle creation in the constant uniform electric field [14,3], in the adiabatic electric field E (t) = E cosh −2 (t/T S ) [15], in the so-called T -constant electric field [16,17], in a periodic alternating in time electric field [18,19], in an exponentially decaying electric field [20], in an exponentially growing and decaying electric fields [21,22] (see Ref. [23] for the review), in a composite electric field [24], and in an inverse-square electric field (an electric field that is inversely proportional to time squared [26]). In the case of x-steps these are particle creation in the Sauter electric field [13], in the so-called L-constant electric field [25], and in the inhomogeneous exponential peak field [27].…”

Radiation Problems Accompanying Carrier Production by an Electric Field in the Graphene

“…In the case of t-steps, these are particle creations in a constant uniform electric field [5][6][7][8], in an adiabatic electric field [9,10], in the so-called T-constant electric field [18,19], in a periodic alternating in time electric field [9,10,20], in an exponentially decaying electric field [21], in an exponentially growing and decaying electric fields [22,23] (see Ref. [24] for the review), in a composite electric field [25], and in an inverse-square electric field [26]. In the case of x-steps, these are particle creation in the Sauter electric field [17], in the so-called L-constant electric field [27], and in the inhomogeneous exponential peak field [28] and inverse-square electric field [26,29].…”

“…[24] for the review), in a composite electric field [25], and in an inverse-square electric field [26]. In the case of x-steps, these are particle creation in the Sauter electric field [17], in the so-called L-constant electric field [27], and in the inhomogeneous exponential peak field [28] and inverse-square electric field [26,29].…”