Shear and bulk viscosities of a photon gas at low temperature

We explore the viscosities of a photon gas by means of the Euler-Heisenberg effective theory and quantum electrodynamics at zero electron chemical potential. We find parametric estimates that show a very large shear viscosity and an extremely small bulk viscosity (reflecting the very weak coupling simultaneously with a very approximate dilatation invariance). The system is of some interest because it exemplifies very neatly the influence of the breaking of scale invariance on the bulk viscosity.