  Within of the framework of semiclassical approximation a general formalism
for deriving an effective current generating bremsstrahlung of arbitrary number
of soft gluons (longitudinal or transverse ones) in scattering of higher-energy
parton off thermal parton in hot quark-gluon plasma with subsequent extension
to two and more scatterers, is obtained. For the case of static color centers
an expression for energy loss induced by usual bremsstrahlung of lowest-order
with allowance for an effective temperature-induced gluon mass and finite mass
of the projectile (heavy quark), is derived. The detailed analysis of
contribution to radiation energy loss associated with existence of effective
three-gluon vertex induced by hot QCD medium, is performed. It is shown that in
general, the bremsstrahlung associated with this vertex have no sharp direction
(as in the case of usual bremsstrahlung) and therefore here, we can expect an
absence of suppression effect due to multiple scattering. For the case of two
color static scattering centers it was shown that the problem of calculation of
bremsstrahlung induced by four-gluon hard thermal loop (HTL) vertex correction
can be reduced to the problem of the calculation of bremsstrahlung induced by
three-gluon HTL correction. It was shown that for limiting value of soft gluon
occupation number $N_{\bf k}\sim 1/\alpha_s$ all higher processes of
bremsstrahlung of arbitrary number of soft gluons become of the same order in
coupling, and the problem of resummation of all relevant contributions to
radiation energy loss of fast parton, arises. An explicit expression for matrix
element of two soft gluon bremsstrahlung in small angles approximation is
obtained.
