  The gluon polarization tensor for the quark-gluon plasma with shear viscosity
is derived with the viscous chromohydrodynamics. The longitudinal and
transverse dielectric functions are evaluated from the gluon polarization
tensor, through which the polarization energy loss suffered by a fast quark
traveling through the viscous quark-gluon plasma is investigated. The numerical
analysis indicates that shear viscosity significantly reduces the polarization
energy loss.
