Viscosity in hot scalar field theory

The spectral representation for general two-point Green functions in thermo field dynamics is used to compute the spectral density of the ${\phi }^2-{\phi }^2$ correlation function in hot ${\phi }^4$ theory. We give a compact 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 dependence of the plasmon width.