On the Vlasov-Einstein Equation and Quantization of Vlasov Equation

In the present paper Wigner equation, Vlasov equation for selfconsistent field and Vlasov-Einstein equation are considered. In the chapter I relationship between solutions of Wigner equation and Vlasov equation is expored. The chapter II is dedicated to the methods of quantization of Vlasov equation in Lagrange variables. In chapter III the Vlasov-Einstein equations for system of particles in a gravitational field are derived. Chapter IV enlightens this problem using Hamiltonian approach. In the final chapter V the Schroedinger type equation for dynamical states of particle in a gravitational field is given and as its particular case Klein-Gordon-Fock equation is obtained.