Shear viscosity of hot QED at finite density from Kubo formula

Within the framework of finite temperature field theory this paper discusses the shear viscosity of hot QED plasma through Kubo formula at one-loop skeleton diagram level with a finite chemical potential. The effective widths(damping rates) are introduced to regulate the pinch singularities. The finite chemical potential, which enhances the contributions to the shear viscosity from the electrons while suppresses those from the photons, finally gives a positive contribution compared to the pure temperature environment. The result agrees with that from the kinetics theory qualitatively.