On the basis of the approximate dynamical equations describing the behaviour of a quark-gluon plasma (QGP) in the semiclassical limit and the Yang-Mills equation, the kinetic equation for longitudinal waves (plasmons) is obtained. The equality of the matrix elements for nonlinear scattering of a plasmon by QGP particles in covariant and temporal gauges are established using the Ward identities. The physical mechanisms defining nonlinear Landau damping are analysed. The problem of the connection between the nonlinear Landau damping rate of longitudinal oscillations with the damping rate obtained within the framework of the hard thermal loops approximation, is considered. It is shown that the gauge-dependent part of the nonlinear Landau damping rate for the plasmons with zero momentum vanishes on mass-shell.

In general line with our first work [Yu.A. Markov, M.A. Markova, Nucl. Phys. A 770 (2006) 162] within the framework of semiclassical approximation a general theory for the scattering processes of soft (anti)quark excitations off hard thermal particles in hot QCD-medium is thoroughly considered. The dynamical equations describing evolution for the usual classical color charge Q a (t) and Grassmann color charges θ i (t), θ †i (t) of hard particle taking into account the soft fermion degree of freedom of the system are suggested. On the basis of these equations and the Blaizot-Iancu equations iterative procedure of calculation of effective currents and sources generating the scattering processes under consideration is defined and their form up to third order in powers of free soft quark field, soft gluon one, and initial values of the color charges of hard particle is explicitly calculated. With use of the generalized Tsytovich principle a connection between matrix elements of the scattering processes and the effective currents and sources is established. In the context of the effective theory suggested for soft and hard fermion excitations new mechanisms of energy losses of high-energy parton propagating through QCD-medium are considered.

Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [Phys. Lett.A 244 (1998) 329] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called q-commutator (q is a primitive cubic root of unity) and a new set of matrices η µ instead of the original matrices β µ of the DKP algebra are introduced. It is shown that in terms of these η µ matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit z → q, where z is some complex deformation parameter entering into the definition of the η-matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out and a comparison with M. Nowakowski's result is performed. A detailed analysis of the general structure for a solution of the first order differential equation for the wave function ψ(x; z) is performed and it is shown that the solution is singular in the z → q limit. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is

On the basis of the Blaizot-Iancu equations, which are a local formulation of the hard thermal loop (HTL) equations of motion for soft fluctuating quark and gluon fields and their induced sources, the coupled kinetic equations for plasminos and plasmons are obtained. The equality of matrix elements for nonlinear scattering of a plasmino by hard particles in covariant and temporal gauges is established by using effective Ward identities. The model problem of the interaction of two infinitely narrow packets with fermion and boson quantum numbers is considered. The kinematical relations between wave vectors of the plasmino and plasmon are derived, when the effective pumping over of the plasma excitation energy from the fermion branch of plasma excitations to the boson branch and vice versa occur. The expression for the nonlinear Landau damping rate of a plasmino at rest is found, and a comparison with a plasmino damping constant obtained within the framework of the hard thermal loop approximation is made. The nonlinear Landau damping rate for normal quark excitations is shown to diverge like $1/\sqrt{q^2}$ near the light cone where $q$ is a four-momentum of excitations, and the improved Blaizot-Iancu equations removing this divergence are proposed.Comment: 32 pages, REVTeX4, 5 eps figures, substantially revised, version to appear in Phys. Rev.

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 lowestorder 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 k ∼ 1/α 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. *