QED Actions in Supercritical Fields
  In the in-out formalism we advance a new method to represent the gamma function for QED actions in supercritical fields, which is complementary to the proper-time integral representation in Phys. Rev. D 78, 105013 (2008) and Phys. Rev. D 84, 065004 (2011). The new method directly yields the QED action in terms of the Hurwitz zeta function in a constant magnetic field and the complex QED action in a constant electric field. The complex action exactly gives the vacuum polarization and the vacuum persistence and thereby the pair-production rate in the electric field. The QED actions exhibit the electromagnetic duality. 
Sang Pyo Kim (Kunsan Natl Univ), Hyun Kyu Lee (Hanyang Univ)
hep-th