Vacuum instability in slowly varying electric fields
  Nonperturbative methods have been well-developed for QED with the so-called t-electric potential steps. In this case a calculation technique is based on the existence of specific exact solutions (in and out solutions) of the Dirac equation. However, there are only few cases when such solutions are known. Here, we demonstrate that for t-electric potential steps slowly varying with time there exist physically reasonable approximations that maintain the nonperturbative character of QED calculations even in the absence of the exact solutions. Defining the slowly varying regime in general terms, we can observe a universal character of vacuum effects caused by a strong electric field. In the present article, we find universal approximate representations for the total density of created pairs and vacuum mean values of the current density and energy-momentum tensor that hold true for arbitrary t-electric potential steps slowly varying with time. These representations do not require knowledge of the corresponding solutions of the Dirac equation, they have a form of simple functionals of a given slowly varying electric field. We establish relations of these representations with leading terms of the derivative expansion approximation. These results allow one to formulate some semiclassical approximations that are not restricted by the smallness of differential mean numbers of created pairs. 
S.P. Gavrilov and D.M. Gitman
hep-th