Statistical properties of states in QED with unstable vacuum
  We study statistical properties of states of massive quantized charged Dirac and Klein-Gordon fields interacting with a background that violates the vacuum stability, first in general terms and then for a special electromagnetic background. As a starting point, we use a nonperturbative expression for the density operators of such fields derived by Gavrilov et al [S.P. Gavrilov, D.M. Gitman, and J.L. Tomazelli, Nucl. Phys. B 795, 645 (2008)]. We construct the reduced density operators for electron and positron subsystems and discuss a decoherence that may occur in the course of the evolution due to an intermediate measurement. By calculating the entropy we study the loss of the information in QED states due to partial reductions and a possible decoherence. Next, we consider the so-called T-constant external electric field as an external background. This exactly solvable example allows us to calculate explicitly all statistical properties of various quantum states of the massive charged fields under consideration. 
S.P. Gavrilov, D.M. Gitman, and A.A. Shishmarev
hep-th