  The expression of the HTL resumed gluon propagator in the light cone gauge is
derived. In the real time mechanism, using the Mandelstam Leibbrant
prescription of $(n\cdot K)^{-1}$, we calculate the transverse and longitudinal
parts of the gluon HTL self-energy and prove the transverse and longitudinal
parts do not have divergence. We also calculate the quark self energy in the
HTL approximation, and find it gauge independent. We analytically calculate the
damping rates of the hard quark and gluon with this HTL resumed gluon
propagator.
