Abstract
Construction of a kinetic equation for a dynamical system interacting with a boson field in the case of spatial inhomogeneity is based on a method expounded in [1–3]. In the present article, it is shown that approaches considered in [1, 2] can be generalized for the case of spatial inhomogeneity. An arbitrary operator function that depends on the momentum and spatial variable is applied for derivation of a kinetic equation. We consider a method of studying an electron-phonon system by means of exclusion of boson operators from corresponding operator equations. In particular, interaction of an electron with a boson field is described by a kinetic equation for a polaron in the case of spatial inhomogeneity. In the relevant limit, a Boltzmann equation for the polaron is obtained.
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