  In this article we study the electrical conductivity in QED using the
resummed 3PI effective action. We work to 3-loop order in the effective action.
We show that the resulting expression for the conductivity is explicitly gauge
invariant, and that the integral equations that resum the pinching and colinear
contributions are produced naturally by the formalism. All leading order terms
are included, without the need for any kind of power counting arguments.
