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In general line with our early works [Yu.A. Markov, M.A. Markova, Nucl. Phys.A770 (2006) 162; 784 (2007) 443] within the framework of a semiclassicalapproximation the general theory of calculation of effective currents andsources generating bremsstrahlung of an arbitrary number of soft quarks andsoft gluons at collision of a high-energy color-charged particle with thermalpartons in a hot quark-gluon plasma, is developed. For the case of one- andtwo-scattering thermal partons with radiation of one or two soft excitations,the effective currents and sources are calculated in an explicit form. In themodel case of `frozen' medium, approximate expressions for energy lossesinduced by the most simple processes of bremsstrahlung of soft quark and softgluon, are derived. On the basis of a conception of the mutual cancellation ofsingularities in the sum of so-called `diagonal' and `off-diagonal'contributions to the energy losses, an effective method of determining colorfactors in scattering probabilities, containing the initial values of Grassmanncolor charges, is suggested. The dynamical equations for Grassmann colorcharges of hard particle used by us early are proved to be insufficient forinvestigation of the higher radiative processes. It is shown that for correctdescription of these processes the given equations should be supplementedsuccessively with the higher-order terms in powers of the soft fermionic field.

Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses