The spectral representation for general two-point Green functions in t
hermo field dynamics is used to compute the spectral density of the ph
i(2)-phi(2) correlation function in hot phi(4) theory. We give a compa
ct derivation of the one-loop contribution to the shear viscosity and
show that it is dominated by low-momentum plasmons. The weak-coupling
behavior of the viscosity is strongly influenced by the momentum depen
dence of the plasmon width.