  In this article we calculate the electrical conductivity in QED using the 2PI
effective action. We use a modified version of the usual 2PI effective action
which is defined with respect to self-consistent solutions of the 2-point
functions. We show that the green functions obtained from this modified
effective action satisfy ward identities and that the conductivity obtained
from the kubo relation is gauge invariant. We work to 3-loop order in the
modified 2PI effective action and show explicitly that the resulting expression
for the conductivity contains the square of the amplitude that corresponds to
all binary collision and production processes.
