Adiabatic perturbation theory for quasilevels

A perturbation theory which is adiabatic with respect to the “proper time” parameter is developed for states with definite quasienergy in a quantum system in a periodic external field. The formulas obtained provide a regular method for writing down the terms of arbitrary order in the perturbation and make it possible to use the algebraic and diagrammatic methods developed in quantum field theory. The behavior of an oscillator in both the absence and the presence of external and parametric resonances is considered as an illustration.