Krylov–Bogoliubov–Mitropolsky averaging used to construct effective Hamiltonians in the theory of strongly correlated electron systems

We show that the Krylov–Bogoliubov–Mitropolsky averaging in the canonical formulation can be used as a method for constructing effective Hamiltonians in the theory of strongly correlated electron systems. As an example, we consider the transition from the Hamiltonians of the Hubbard and Anderson models to the respective Hamiltonians of the $t$–$J$ and Kondo models. This is a very general method, has several advantages over other methods, and can be used to solve a wide range of problems in the physics of correlated systems.