Vacuum Persistence and Inversion of Spin Statistics in Strong QED

The vacuum persistence can be written as the Bose-Einstein distribution in spinor QED and as the Fermi-Dirac distribution in scalar QED exactly in a constant electric field and approximately in time-varying electric fields. The inverse temperature is determined by the period of charged particle in the Euclidean time and the negative chemical potential by the ratio of the worldline instanton to the inverse temperature. The negativity of chemical potential is due to the vacuum instability under strong electric fields. The inversion of spin statistics in the vacuum persistence is a consequence of the Bogoliubov relations for fermions and bosons.