ABSTRACT
This chapter generalizes works by N.N. Bogolubov and N.N. Bogolubov, Jr. [1,6], and is written with the aim of formulating methods of investigation of the electron-phonon system and the elimination of phonon operators from the corresponding kinetic equations. In particular, a kinetic equation is derived for the interaction of an electron with a phonon field. Moreover, under the proper approximation, the exact Boltzmann equation for the polaron system follows from this kinetic equation. Methods of calculation of the response functions (impedance and admittance), based on the "approximating" Hamiltonian with linear interaction, are also proposed. The equilibrium density probability function of the particle is also calculated.
