Nonperturbative QED effective action at finite temperature

We propose a novel method for the effective action of spinor and scalar QED at finite temperature in time-dependent electric fields, where charged pairs evolve in a nonadiabatic way. The imaginary part of the effective action consists of thermal loops of the Fermi-Dirac or Bose-Einstein distribution for the initial thermal ensemble, weighted with factors of the Bogoliubov coefficients for quantum effects. And the real part of the effective action is determined by the mean number of produced pairs and vacuum polarization at zero temperature. In the weak-field limit, the mean number of produced pairs is shown twice the imaginary part. We explicitly find the finite-temperature effective action in a constant electric field.The authors would like to thank Holger Gies for useful information and comments, Ismail Zahed for useful discussions, and Sergey Gavrilov for useful comments. S. P. K. would like to thank W-Y. Pauchy Hwang for the warm hospitality at National Taiwan University, where part of this paper was written. The work of S. P. K. was supported by the Korea Research Foundation (KRF) Grant funded by the Korea Ministry of Education, Science and Technology (2009-0075-773) and the work of H. K. L. was supported by the World Class University Program (R33-2008-000-10087-0) of the Korea Ministry of Education, Science and Technology