Derivation of kinetic equations in the statistical $T$-matrix approximation

In contrast to the previous paper of the authors, allowance is made for the line width in the eikonal propagators and an eikonal amplitude of quasiparticle scattering is obtained for a general dispersion law in the form of a Lorentz curve. The explicit form is obtained of a generalized kinetic equation with self-consistent field, dissipative terms, and collision integral with cross section that depends on the total momentum, the statistics, and the damping of the quasiparticles. The corresponding transport equations suitable for describing relaxation in dense media are given. A statisticaI $T$-matrix of three-particle correlations is introduced and its eikonal approximations and the corresponding expressions for the generalized three-particle collision integrals are proposed.