Effective energy-momentum tensor of strong-field QED with unstable   vacuum
  We study the influence of a vacuum instability on the effective energy-momentum tensor (EMT) of QED, in the presence of a quasiconstant external electric field, by means of the relevant Green functions. In the case when the initial vacuum, |0,in>, differs essentially from the final vacuum, |0,out>, we find explicitly and compared both the vacuum average value of EMT, <0,in|T_{\mu \nu}|0,in>, and the matrix element, <0,out|T_{\mu \nu}|0,in>. In the course of the calculation we solve the problem of the special divergences connected with infinite time T of acting of the constant electric field. The EMT of pair created by an electric field from the initial vacuum is presented. The relations of the obtained expressions to the Euler-Heisenberg's effective action are established. 
S. P. Gavrilov