Leading Order QED Electrical Conductivity from the 3PI Effective Action

TL;DR

This paper calculates the electrical conductivity in QED using a 3PI effective action approach, ensuring gauge invariance and including all leading order terms without additional assumptions.

Contribution

It introduces a gauge-invariant method to compute QED conductivity at 3-loop order using the 3PI effective action, naturally deriving integral equations for key contributions.

Findings

Gauge-invariant conductivity expression derived

Integral equations for pinching and colinear contributions obtained

All leading order terms included without power counting

Abstract

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.