  The microscopic formulae of the bulk viscosity $\zeta $ and the corresponding
relaxation time $\tau_{\Pi}$ in causal dissipative relativistic fluid dynamics
are derived by using the projection operator method. In applying these formulae
to the pionic fluid, we find that the renormalizable energy-momentum tensor
should be employed to obtain consistent results. In the leading order
approximation in the chiral perturbation theory, the relaxation time is
enhanced near the QCD phase transition and $\tau_{\Pi}$ and $\zeta $ are
related as $\tau_{\Pi}=\zeta /[\beta \{(1/3-c_{s}^{2})(\epsilon +P)-2(\epsilon
-3P)/9\}]$, where $\epsilon $, $P$ and $c_{s}$ are the energy density, pressure
and velocity of sound, respectively. The predicted $\zeta $ and $% \tau_{\Pi}$
should satisfy the so-called causality condition. We compare our result with
the results of the kinetic calculation by Israel and Stewart and the string
theory, and confirm that all the three approaches are consistent with the
causality condition.
