  Using the Schwinger-Keldysh (closed time path or CTP) and Feynman-Vernon
influence functional formalisms we obtain an expression for the influence
functional in terms of Bogoliubov coefficients for the case of spinor quantum
electrodynamics. Then we derive a CTP effective action in semiclassical
approximation and its cumulant expansion. Using it we obtain a equation for the
description of the charged particle creation in electric field and of
backreaction of charged quantum fields and their fluctuations on time evolution
of this electric field. Also an intimate connection between CTP effective
action and decoherence functional will allow us to analyze how macroscopic
electromagnetic fields are ``measured'' through interaction with charges and
thereby rendered classical.
