  We show how to compute transport coefficients in gauge theories by
considering the expansion of the Kubo formulas in terms of ladder diagrams in
the imaginary time formalism. All summations over Matsubara frequencies are
performed and the analytical continuation to get the retarded correlators is
done. As an illustration of the procedure, we present a derivation of the
transport equation for the shear viscosity in the scalar theory. Assuming the
Hard Thermal Loop approximation for the screening of distant collisions of the
hard particles in the plasma, we derive a couple of integral equations for the
effective vertices which, to logarithmic accuracy, are shown to be identical to
the linearized Boltzmann equations previously found by Arnold, Moore and Yaffe.
