  The microscopic formulas for the shear viscosity $\eta$, the bulk viscosity
$\zeta$, and the corresponding relaxation times $\tau_\pi$ and $\tau_\Pi$ of
causal dissipative relativistic fluid-dynamics are obtained at finite
temperature and chemical potential by using the projection operator method. The
non-triviality of the finite chemical potential calculation is attributed to
the arbitrariness of the operator definition for the bulk viscous pressure.We
show that, when the operator definition for the bulk viscous pressure $\Pi$ is
appropriately chosen, the leading-order result of the ratio, $\zeta$ over
$\tau_\Pi$, coincides with the same ratio obtained at vanishing chemical
potential. We further discuss the physical meaning of the time-convolutionless
(TCL) approximation to the memory function, which is adopted to derive the main
formulas. We show that the TCL approximation violates the time reversal
symmetry appropriately and leads results consistent with the quantum master
equation obtained by van Hove. Furthermore, this approximation can reproduce an
exact relation for transport coefficients obtained by using the f-sum rule
derived by Kadanoff and Martin. Our approach can reproduce also the result in
Baier et al.(2008) Ref. \cite{con} by taking into account the next-order
correction to the TCL approximation, although this correction causes several
problems.
