  Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu,
Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP),
two-particle-irreducible (2PI) effective action we show how to compute from
first principles the shear and bulk viscosity functions in the
hydrodynamic-thermodynamic regime. For a real scalar field with $\lambda \Phi
^{4}$ self-interaction we need to include 4 loop graphs in the equation of
motion. This work provides a microscopic field-theoretical basis to the
``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G.
Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity
reproduces their expression derived from linear response theory and the
imaginary-time formalism of thermal field theory. Though unavoidably involved
in calculations of this sort, we feel that the approach using fundamental
quantum kinetic field theory is conceptually clearer and methodically simpler
than the effective kinetic theory approach, as the success of the latter
requires clever rendition of diagrammatic resummations which is neither
straightforward nor failsafe. Moreover, the method based on the CTP-2PI
effective action illustrated here for a scalar field can be formulated entirely
in terms of functional integral quantization, which makes it an appealing
method for a first-principles calculation of transport functions of a thermal
non-abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion
collisions.
