  Hydrodynamic transport coefficients may be evaluated from first principles in
a weakly coupled scalar field theory at arbitrary temperature. In a theory with
cubic and quartic interactions, the infinite class of diagrams which contribute
to the leading weak coupling behavior are identified and summed. The resulting
expression may be reduced to a single linear integral equation, which is shown
to be identical to the corresponding result obtained from a linearized
Boltzmann equation describing effective thermal excitations with temperature
dependent masses and scattering amplitudes. The effective Boltzmann equation is
valid even at very high temperature where the thermal lifetime and mean free
path are short compared to the Compton wavelength of the fundamental particles.
Numerical results for the shear and the bulk viscosities are presented.
