  The electric current density of fermions in the presence of an external
electric field is determined through the utilization of a time-ordered
Schwinger propagator. The study encompasses the necessary conditions for
establishing a well-defined time-ordered propagator within the Schwinger
formalism, specifically concentrating on constant and uniform electromagnetic
fields. Within this theoretical framework, the introduction of the Schwinger
phase induces a chemical potential, resulting in non-zero values for the
electric current and charge number density. Consequently, the dependence of
electric conductivity on the strength of the electric field and the charge
number density is investigated.
