  Our previous results on the nonperturbative calculations of the mean current
and of the energy-momentum tensor in QED with the T-constant electric field are
generalized to arbitrary dimensions. The renormalized mean values are found;
the vacuum polarization and particle creation contributions to these mean
values are isolated in the large T-limit, the vacuum polarization contributions
being related to the one-loop effective Euler-Heisenberg Lagrangian.
Peculiarities in odd dimensions are considered in detail. We adapt general
results obtained in 2+1 dimensions to the conditions which are realized in the
Dirac model for graphene. We study the quantum electronic and energy transport
in the graphene at low carrier density and low temperatures when quantum
interference effects are important. Our description of the quantum transport in
the graphene is based on the so-called generalized Furry picture in QED where
the strong external field is taken into account nonperturbatively; this
approach is not restricted to a semiclassical approximation for carriers and
does not use any statistical assumtions inherent in the Boltzmann transport
theory. In addition, we consider the evolution of the mean electromagnetic
field in the graphene, taking into account the backreaction of the matter field
to the applied external field. We find solutions of the corresponding
Dirac-Maxwell set of equations and with their help we calculate the effective
mean electromagnetic field and effective mean values of the current and the
energy-momentum tensor. The nonlinear and linear I-V characteristics
experimentally observed in both low and high mobility graphene samples is quite
well explained in the framework of the proposed approach, their peculiarities
being essentially due to the carrier creation from the vacuum by the applied
electric field.
