The time-dependent variational approach to the pure Yang-Mills gauge theory,
especially a color su(3) gauge theory, is formulated in the functional
Schroedinger picture with a Gaussian wave functional approximation. The
equations of motion for the quantum gauge fields are formulated in the
Liouville-von Neumann form. This variational approach is applied in order to
derive the transport coefficients, such as the shear viscosity, for the pure
gluonic matter by using the linear response theory. As a result, the
contribution to the shear viscosity from the quantum gluons is zero up to the
lowest order of the coupling g in the quantum gluonic matter.Comment: 19 pages, no figures, using PTPTeX.cl