Leading Order Calculation of Shear Viscosity in Hot Quantum Electrodynamics from Diagrammatic Methods

TL;DR

This paper calculates the shear viscosity of hot QED at leading order using diagrammatic methods, ensuring gauge invariance and including effects like Landau-Pomeranchuk-Migdal through resummation.

Contribution

It introduces a gauge-invariant diagrammatic approach to compute shear viscosity in hot QED, connecting integral equations with kinetic theory and including collinear effects.

Findings

Derived integral equations for shear viscosity using Ward identities.

Established equivalence with linearized Boltzmann equations.

Included all relevant scattering processes for accurate leading-order calculation.

Abstract

We compute the shear viscosity at leading order in hot Quantum Electrodynamics. Starting from the Kubo relation for shear viscosity, we use diagrammatic methods to write down the appropriate integral equations for bosonic and fermionic effective vertices. We also show how Ward identities can be used to put constraints on these integral equations. One of our main results is an equation relating the kernels of the integral equations with functional derivatives of the full self-energy; it is similar to what is obtained with two-particle-irreducible effective action methods. However, since we use Ward identities as our starting point, gauge invariance is preserved. Using these constraints obtained from Ward identities and also power counting arguments, we select the necessary diagrams that must be resummed at leading order. This includes all non-collinear (corresponding to 2 to 2 scatterings) and collinear (corresponding to 1+N to 2+N collinear scatterings) rungs responsible for the Landau-Pomeranchuk-Migdal effect. We also show the equivalence between our integral equations obtained from quantum field theory and the linearized Boltzmann equations of Arnold, Moore and Yaffe obtained using effective kinetic theory.